Lesson 9
Finding Distances in the Coordinate Plane
Let’s find distances in the coordinate plane.
Problem 1
The right triangles are drawn in the coordinate plane, and the coordinates of their vertices are labeled. For each right triangle, label each leg with its length.
![3 right triangles on a xy plane.](https://staging-cms-im.s3.amazonaws.com/ZzG6WVPouYVbu2Epdkay7sH1?response-content-disposition=inline%3B%20filename%3D%228-8.8.C11.PP.Image.0001.png%22%3B%20filename%2A%3DUTF-8%27%278-8.8.C11.PP.Image.0001.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T132144Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=5b1dfce6e4106736e4c75fc85467f388fbeeeb3fa3e4fe1b0da7327e0ed70a30)
Problem 2
Find the distance between each pair of points. If you get stuck, try plotting the points on graph paper.
- \(M=(0,\text-11)\) and \(P=(0,2)\)
- \(A=(0,0)\) and \(B=(\text-3, \text-4)\)
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\(C=(8,0)\) and \(D=(0, \text-6)\)
Problem 3
- Find an object that contains a right angle. This can be something in nature or something that was made by humans or machines.
- Measure the two sides that make the right angle. Then measure the distance from the end of one side to the end of the other.
- Draw a diagram of the object, including the measurements.
- Use the Pythagorean Theorem to show that your object really does have a right angle.
Problem 4
Which line has a slope of 0.625, and which line has a slope of 1.6? Explain why the slopes of these lines are 0.625 and 1.6.
![Two lines on a grid that intersect at a point. 2nd point on Top line is 8 up and 5 right from 1st point. 2nd point on bottom line is 5 up and 8 right from 1st point.](https://staging-cms-im.s3.amazonaws.com/rkQkdRusemddJnCSpFMqUcUV?response-content-disposition=inline%3B%20filename%3D%228-8.2.C.PP.Image.11.png%22%3B%20filename%2A%3DUTF-8%27%278-8.2.C.PP.Image.11.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T132144Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=46a53bcc5418090b4169ff9c6d19a4781a85a6c017d6ee4f2d4457cddfd52f16)
Problem 5
Write an equation for the graph.
![Horizontal axis, 0 to 4, 1’s. Vertical axis, 0 to 6, 1’s. Line with slope=2, y intercept =1.5.](https://staging-cms-im.s3.amazonaws.com/d4Ub2LXD2awc8GSmFzfoZsWn?response-content-disposition=inline%3B%20filename%3D%228-8.3.B7.PP.graph2.png%22%3B%20filename%2A%3DUTF-8%27%278-8.3.B7.PP.graph2.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T132144Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=435b6ffddd08274e9164c37124766ec07fe53c4da6115167be09afe34dd5cd97)