# The Coordinate Plane (Geometry 2_4)

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- The Coordinate Plane You will learn to name and graph ordered pairs on a coordinate plane. What You'll Learn In coordinate geometry, grid paper is used to locate points. The plane of the grid is called the coordinate plane .
- The Coordinate Plane You will learn to name and graph ordered pairs on a coordinate plane. What You'll Learn In coordinate geometry, grid paper is used to locate points. The plane of the grid is called the coordinate plane . y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3
- The Coordinate Plane The horizontal number line is called the ______. y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3 O
- The Coordinate Plane The horizontal number line is called the ______. x-axis y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3 O
- The Coordinate Plane The horizontal number line is called the ______. x-axis The vertical number line is called the ______. y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3 O
- The Coordinate Plane The horizontal number line is called the ______. x-axis The vertical number line is called the ______. y-axis y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3 O
- The Coordinate Plane The horizontal number line is called the ______. x-axis The vertical number line is called the ______. y-axis The point of intersection of the two axes is called the _____. y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3 O
- The Coordinate Plane The horizontal number line is called the ______. x-axis The vertical number line is called the ______. y-axis The point of intersection of the two axes is called the _____. origin y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3 O
- The Coordinate Plane The horizontal number line is called the ______. x-axis The vertical number line is called the ______. y-axis The point of intersection of the two axes is called the _____. origin The two axes separate the plane into four regions called _________. y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3
- The Coordinate Plane The horizontal number line is called the ______. x-axis The vertical number line is called the ______. y-axis The point of intersection of the two axes is called the _____. origin The two axes separate the plane into four regions called _________. quadrants y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3 Quadrant I (+, +) Quadrant II ( – , +) Quadrant III ( – , – ) Quadrant IV ( + , – )
- The Coordinate Plane An ordered pair of real numbers, called coordinates of a point, locates a point in the coordinate plane.
- The Coordinate Plane An ordered pair of real numbers, called coordinates of a point, locates a point in the coordinate plane. Each ordered pair corresponds to EXACTLY ________ in the coordinate plane.
- The Coordinate Plane An ordered pair of real numbers, called coordinates of a point, locates a point in the coordinate plane. Each ordered pair corresponds to EXACTLY ________ in the coordinate plane. one point
- The Coordinate Plane An ordered pair of real numbers, called coordinates of a point, locates a point in the coordinate plane. Each ordered pair corresponds to EXACTLY ________ in the coordinate plane. one point The point in the coordinate plane is called the graph of the ordered pair.
- The Coordinate Plane An ordered pair of real numbers, called coordinates of a point, locates a point in the coordinate plane. Each ordered pair corresponds to EXACTLY ________ in the coordinate plane. one point The point in the coordinate plane is called the graph of the ordered pair. Locating a point on the coordinate plane is called _______ the ordered pair.
- The Coordinate Plane An ordered pair of real numbers, called coordinates of a point, locates a point in the coordinate plane. Each ordered pair corresponds to EXACTLY ________ in the coordinate plane. one point The point in the coordinate plane is called the graph of the ordered pair. Locating a point on the coordinate plane is called _______ the ordered pair. graphing
- The Coordinate Plane An ordered pair of real numbers, called coordinates of a point, locates a point in the coordinate plane. Each ordered pair corresponds to EXACTLY ________ in the coordinate plane. one point The point in the coordinate plane is called the graph of the ordered pair. Locating a point on the coordinate plane is called _______ the ordered pair. graphing Each point in a coordinate plane corresponds to exactly one __________________________. Each ordered pair of real numbers corresponds to exactly one __________________________. Postulate 2 – 4 Completeness Property for Points in the Plane
- The Coordinate Plane An ordered pair of real numbers, called coordinates of a point, locates a point in the coordinate plane. Each ordered pair corresponds to EXACTLY ________ in the coordinate plane. one point The point in the coordinate plane is called the graph of the ordered pair. Locating a point on the coordinate plane is called _______ the ordered pair. graphing ordered pair of real numbers Each point in a coordinate plane corresponds to exactly one __________________________. Each ordered pair of real numbers corresponds to exactly one __________________________. Postulate 2 – 4 Completeness Property for Points in the Plane
- The Coordinate Plane An ordered pair of real numbers, called coordinates of a point, locates a point in the coordinate plane. Each ordered pair corresponds to EXACTLY ________ in the coordinate plane. one point The point in the coordinate plane is called the graph of the ordered pair. Locating a point on the coordinate plane is called _______ the ordered pair. graphing ordered pair of real numbers point in the coordinate plane Each point in a coordinate plane corresponds to exactly one __________________________. Each ordered pair of real numbers corresponds to exactly one __________________________. Postulate 2 – 4 Completeness Property for Points in the Plane
- The Coordinate Plane Graphing an ordered pair, (point): ( x , y ) Graph point A at (4, 3) The first number, 4, is called the ___________. x-coordinate It tells the number of units the point lies to the __________ of the origin. y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3
- The Coordinate Plane Graphing an ordered pair, (point): ( x , y ) Graph point A at (4, 3) The first number, 4, is called the ___________. x-coordinate It tells the number of units the point lies to the __________ of the origin. left or right y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3
- The Coordinate Plane Graphing an ordered pair, (point): ( x , y ) Graph point A at (4, 3) The first number, 4, is called the ___________. x-coordinate It tells the number of units the point lies to the __________ of the origin. The second number, 3, is called the ___________. y-coordinate It tells the number of units the point lies _____________ the origin. left or right y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3
- The Coordinate Plane Graphing an ordered pair, (point): ( x , y ) Graph point A at (4, 3) The first number, 4, is called the ___________. x-coordinate It tells the number of units the point lies to the __________ of the origin. The second number, 3, is called the ___________. y-coordinate It tells the number of units the point lies _____________ the origin. left or right above or below (4, 3) y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3
- The Coordinate Plane Graphing an ordered pair, (point): ( x , y ) Graph point A at (4, 3) The first number, 4, is called the ___________. x-coordinate It tells the number of units the point lies to the __________ of the origin. The second number, 3, is called the ___________. y-coordinate It tells the number of units the point lies _____________ the origin. left or right above or below (4, 3) What is the coordinate of the origin? y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3
- The Coordinate Plane Graphing an ordered pair, (point): ( x , y ) Graph point A at (4, 3) The first number, 4, is called the ___________. x-coordinate It tells the number of units the point lies to the __________ of the origin. The second number, 3, is called the ___________. y-coordinate It tells the number of units the point lies _____________ the origin. left or right above or below (4, 3) What is the coordinate of the origin? y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3 (0, 0)
- The Coordinate Plane Graphing an ordered pair, (point): ( x , y ) Graph point B at (2, –3) y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3
- The Coordinate Plane Graphing an ordered pair, (point): ( x , y ) Graph point B at (2, –3) The first number, 2, is called the ___________. x-coordinate It tells the number of units the point lies to the __________ of the origin. y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3
- The Coordinate Plane Graphing an ordered pair, (point): ( x , y ) Graph point B at (2, –3) The first number, 2, is called the ___________. x-coordinate It tells the number of units the point lies to the __________ of the origin. left or right y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3
- The Coordinate Plane Graphing an ordered pair, (point): ( x , y ) Graph point B at (2, –3) The first number, 2, is called the ___________. x-coordinate It tells the number of units the point lies to the __________ of the origin. The second number, –3, is called the ___________. y-coordinate It tells the number of units the point lies _____________ the origin. left or right y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3
- The Coordinate Plane Graphing an ordered pair, (point): ( x , y ) Graph point B at (2, –3) The first number, 2, is called the ___________. x-coordinate It tells the number of units the point lies to the __________ of the origin. The second number, –3, is called the ___________. y-coordinate It tells the number of units the point lies _____________ the origin. left or right above or below (2, – 3) y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3
- The Coordinate Plane Give the coordinates of the points A, B, C, & D Point A(x, y) = Point B(x, y) = Point C(x, y) = Point D(x, y) = A D C B y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3 B C D A
- The Coordinate Plane Name the points A, B, C, & D Point A(x, y) = Point B(x, y) = Point C(x, y) = Point D(x, y) = A (3, 2) D C B ( – 3, – 2) ( – 3, 2) (3, – 2) y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3 (–3, 2) B (–3, –2) C (3, –2) D (3, 2) A
- The Coordinate Plane Point A(x, y) = A(2, 4) Point B(x, y) = B(2, 0) Point C(x, y) = C(2, – 3) Point D(x, y) = D(2, – 5)
- On a piece of grid paper draw lines representing the x-axis and the y-axis.

- Graph :

- The Coordinate Plane Point A(x, y) = A(2, 4) Point B(x, y) = B(2, 0) Point C(x, y) = C(2, – 3) Point D(x, y) = D(2, – 5)
- On a piece of grid paper draw lines representing the x-axis and the y-axis.

- Graph :

- The Coordinate Plane Point A(x, y) = A(2, 4) Point B(x, y) = B(2, 0) Point C(x, y) = C(2, – 3) Point D(x, y) = D(2, – 5)
- On a piece of grid paper draw lines representing the x-axis and the y-axis.

- Graph :

- The Coordinate Plane Point A(x, y) = A(2, 4) Point B(x, y) = B(2, 0) Point C(x, y) = C(2, – 3) Point D(x, y) = D(2, – 5)
- On a piece of grid paper draw lines representing the x-axis and the y-axis.

- Graph :

- The Coordinate Plane Point A(x, y) = A(2, 4) Point B(x, y) = B(2, 0) Point C(x, y) = C(2, – 3) Point D(x, y) = D(2, – 5)
- On a piece of grid paper draw lines representing the x-axis and the y-axis.

- Graph :

- The Coordinate Plane Point A(x, y) = A(2, 4) Point B(x, y) = B(2, 0) Point C(x, y) = C(2, – 3) Point D(x, y) = D(2, – 5)
- On a piece of grid paper draw lines representing the x-axis and the y-axis.

- Graph :

- The Coordinate Plane Point A(x, y) = A(2, 4) Point B(x, y) = B(2, 0) Point C(x, y) = C(2, – 3) Point D(x, y) = D(2, – 5)
- On a piece of grid paper draw lines representing the x-axis and the y-axis.

- Graph :

- The Coordinate Plane Point W(x, y) = W( –4 , – 4) Point X(x, y) = X( –2 , –4 ) Point Y(x, y) = Y(0, –4 ) Point Z(x, y) = Z(3, –4 )
- Graph :

- The Coordinate Plane Point W(x, y) = W( –4 , – 4) Point X(x, y) = X( –2 , –4 ) Point Y(x, y) = Y(0, –4 ) Point Z(x, y) = Z(3, –4 )
- Graph :

- The Coordinate Plane Point W(x, y) = W( –4 , – 4) Point X(x, y) = X( –2 , –4 ) Point Y(x, y) = Y(0, –4 ) Point Z(x, y) = Z(3, –4 )
- Graph :

- The Coordinate Plane Point W(x, y) = W( –4 , – 4) Point X(x, y) = X( –2 , –4 ) Point Y(x, y) = Y(0, –4 ) Point Z(x, y) = Z(3, –4 )
- Graph :

- The Coordinate Plane Point W(x, y) = W( –4 , – 4) Point X(x, y) = X( –2 , –4 ) Point Y(x, y) = Y(0, –4 ) Point Z(x, y) = Z(3, –4 )
- Graph :

- The Coordinate Plane Point W(x, y) = W( –4 , – 4) Point X(x, y) = X( –2 , –4 ) Point Y(x, y) = Y(0, –4 ) Point Z(x, y) = Z(3, –4 )
- Graph :

- The Coordinate Plane Point W(x, y) = W( –4 , – 4) Point X(x, y) = X( –2 , –4 ) Point Y(x, y) = Y(0, –4 ) Point Z(x, y) = Z(3, –4 )
- Graph :

- The Coordinate Plane Point W(x, y) = W( –4 , – 4) Point X(x, y) = X( –2 , –4 ) Point Y(x, y) = Y(0, –4 ) Point Z(x, y) = Z(3, –4 )
- Graph :

- The Coordinate Plane If a and b are real numbers, a vertical line contains all points (x, y) such that _____ and a horizontal line contains all points (x, y) such that _____ Theorem 2 – 4
- The Coordinate Plane x = a y = b If a and b are real numbers, a vertical line contains all points (x, y) such that _____ and a horizontal line contains all points (x, y) such that _____ Theorem 2 – 4
- The Coordinate Plane x = a y = b Graph the lines: x = –3 If a and b are real numbers, a vertical line contains all points (x, y) such that _____ and a horizontal line contains all points (x, y) such that _____ Theorem 2 – 4 y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3
- The Coordinate Plane x = a y = b Graph the lines: x = –3 If a and b are real numbers, a vertical line contains all points (x, y) such that _____ and a horizontal line contains all points (x, y) such that _____ Theorem 2 – 4 y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3
- The Coordinate Plane x = a y = b Graph the lines: x = –3 y = 2 If a and b are real numbers, a vertical line contains all points (x, y) such that _____ and a horizontal line contains all points (x, y) such that _____ Theorem 2 – 4 y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3
- The Coordinate Plane x = a y = b Graph the lines: x = –3 y = 2 If a and b are real numbers, a vertical line contains all points (x, y) such that _____ and a horizontal line contains all points (x, y) such that _____ Theorem 2 – 4 y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3
- The Coordinate Plane x = a y = b Graph the lines: x = –3 y = 2 Graph the point of intersection of these lines. If a and b are real numbers, a vertical line contains all points (x, y) such that _____ and a horizontal line contains all points (x, y) such that _____ Theorem 2 – 4 y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3
- The Coordinate Plane x = a y = b Graph the lines: x = –3 y = 2 Graph the point of intersection of these lines. If a and b are real numbers, a vertical line contains all points (x, y) such that _____ and a horizontal line contains all points (x, y) such that _____ Theorem 2 – 4 y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3 (–3, 2)
- The Coordinate Plane End of Lesson