Question

a designer plans a wallpaper border using triangles. the designer draws △jkl in the coordinate plane. then they translate △jkl 6 units to the right to form △jkl. a. what are the coordinates of the vertices of △jkl? show your work. b. check your answer to problem 3a. show your work.

Explanation:

Step1: Recall translation rule

For a translation 6 units to the right in the coordinate - plane, we add 6 to the x - coordinate of each point while keeping the y - coordinate the same.

Step2: Find coordinates of J'

Given J(-4,5), new x - coordinate is - 4+6 = 2, y - coordinate remains 5. So J'(2,5).

Step3: Find coordinates of K'

Given K(-2,1), new x - coordinate is - 2+6 = 4, y - coordinate remains 1. So K'(4,1).

Step4: Find coordinates of L'

Given L(-4,2), new x - coordinate is - 4+6 = 2, y - coordinate remains 2. So L'(2,2).

Step5: Check the answers

We can reverse the translation. To go from J'(2,5) back to J, we subtract 6 from the x - coordinate: 2 - 6=-4, y - coordinate is 5, which is the original J(-4,5).
For K'(4,1), 4 - 6=-2, y - coordinate is 1, which is the original K(-2,1).
For L'(2,2), 2 - 6=-4, y - coordinate is 2, which is the original L(-4,2).

Answer:

J'(2,5), K'(4,1), L'(2,2)