1.8 The Coordinate Plane

You will learn to name and graph ordered pairs on a coordinate plane. What You'll Learn You will learn to name and graph ordered pairs on a coordinate plane. y x 5 -4 -2 1 3 -5 -1 4 -3 2 In coordinate geometry, grid paper is used to locate points.

You will learn to find the distance of a line segment. What You'll Learn You will learn to find the distance of a line segment. B A The distance of a line segment AB is found by the formula

You will learn to find the coordinates of the midpoint of a segment. What You'll Learn You will learn to find the coordinates of the midpoint of a segment. B A C The midpoint of a line segment AB is the point C that ______ the segment. bisects

The horizontal number line is called the ______. x-axis Lets’ look at the grid. y x 5 -4 -2 1 3 -5 -1 4 -3 2 Quadrant II (–, +) Quadrant I (+, +) O Quadrant III (–, –) Quadrant IV (+, –) 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 Lets’ look at the grid. y x 5 -4 -2 1 3 -5 -1 4 -3 2 Quadrant II (–, +) Quadrant I (+, +) O Quadrant III (–, –) Quadrant IV (+, –) The point of intersection of the two axes is called the _____. origin The two axes separate the plane into four regions called _________. quadrants

Now, see if you can name the points. B B A A C C D D Point A(x, y) = 5 -4 -2 1 3 -5 -1 4 -3 2 (–3, 2) B B A (3, 2) A C (–3, –2) C D (3, –2) D Point A(x, y) = (3, 2) Point C(x, y) = (–3, –2) Point B(x, y) = (–3, 2) Point D(x, y) = (3, –2)

OK, It’s your turn On a piece of grid paper draw lines representing the x-axis and the y-axis. Graph : A(2, 4) y x 5 -4 -2 1 3 -5 -1 4 -3 2 B(2, 0) A C(2, –3) D(2, –5) B C D

What do you notice about the graphs of these points? OK, It’s your turn Consider these questions: What do you notice about the graphs of these points? x = 2 They lie on a vertical line. y x 5 -4 -2 1 3 -5 -1 4 -3 2 A B C D

What do you notice about the x-coordinates of these points? OK, It’s your turn Consider these questions: What do you notice about the x-coordinates of these points? A(2, 4) y x 5 -4 -2 1 3 -5 -1 4 -3 2 B(2, 0) A C(2, –3) D(2, –5) B They are the same number. C D

OK, It’s your turn Consider these questions: Write a general statement about ordered pairs that have the same x-coordinate. They lie on a vertical line that intersects the x-axis at the x-coordinate. y x 5 -4 -2 1 3 -5 -1 4 -3 2 A B C D

Find the distance between two points. How about the distance between two points Find the distance between two points. (-2,5) and (8,3) d=10.19803903

Find the midpoint between two points. Lets’ look at finding a midpoint. Find the midpoint between two points. (0.45,7) and (-0.3,-9) (0.075,-1)

Find the midpoint, C(x, y), of a segment on the coordinate plane. y x 10 -1 2 4 6 8 -2 3 7 1 5 9 x = 1 x = 9 A(1, 7) B(9, 3) y = 7 C(5, 5) y x y = 3

Graph A(1, 1) and B(7, 9) Draw AB Find the midpoint of AB. B(7, 9) C y x 10 -1 2 4 6 8 -2 3 7 1 5 9 B(7, 9) Find the midpoint of AB. C C(4, 5) A(1, 1)

Suppose C(3, 5) is the midpoint of AB. Find the coordinate of B. x-coordinate of B y-coordinate of B B(-1, 8) Replace x1 with 7 and y1 with 2 B(x, y) is somewhere over there. C(3, 5) midpoint A(7, 2) Multiply each side by 2 Add or subtract to isolate the variable

In the figure, B is the midpoint of AC. Find the value of x. 5x - 6 2x C B A Check! Since B is the midpoint: AB = BC AB = 5x – 6 = 5(2) – 6 = 10 – 6 = 4 Write the equation involving x: 5x – 6 = 2x Solve for x: 5x – 2x – 6 = 2x – 2x 3x – 6 + 6 = 0 + 6 3x = 6 x = 2 BC = 2x = 2(2) = 4

Assignment

1.8 The Coordinate Plan A B Geometry y x 5 -1 2 4 -2 1 -3 3 1. Name the coordinates of each point. A 2. Graph point C at (0, –4). 3. Graph x = –4. B 4. Graph y = 2. 5. Graph and label the intersection of x = –4 and y = 2 6. DF is bisected at point E, and DF = 8. What do you know about the lengths of DE and EF ? 7. In the figure below, R is the midpoint of QS. Find the value of d. 8. True or False: If AB  CD, then CD  AB. 9. True or False: If AB  BC, then B is the midpoint of AC. d + 4 3d S R Q 10. Find the distance: (-4,9),(1,-3) 11. Find the midpoint: (9,-2),(12,-14)

1.8 The Coordinate Plan A B Geometry y x 5 -1 2 4 -2 1 -3 3 1. Name the coordinates of each point. A = (2, 0) B = (3, –2) A 2. Graph point C at (0, –4). 3. Graph x = –4. B 4. Graph y = 2. 5. Graph and label the intersection of x = –4 and y = 2 6. DF is bisected at point E, and DF = 8. What do you know about the lengths of DE and EF ? 7. In the figure below, R is the midpoint of QS. Find the value of d. 8. True or False: If AB  CD, then CD  AB. 9. True or False: If AB  BC, then B is the midpoint of AC. d + 4 3d S R Q 10. Find the distance: (-4,9),(1,-3) 11. Find the midpoint: (9,-2),(12,-14)