Question

the vertices of △abc are located at a(2,6), b(3, - 1), and c(-2,5). the vertices of △xyz are located at x(3,1), y(4, - 6), and z(-1,0). describe a sequence of translations to show that △abc is congruent to △xyz. > select from the drop - down menus to complete the sentence. you can translate each vertex of △abc and to create △xyz.

Explanation:

Step1: Find the change in x - coordinates

For the x - coordinates:
Let's consider the x - coordinates of corresponding vertices. For example, comparing the x - coordinates of A(2,6) and X(3,1). The change in x is \(3 - 2=1\).

Step2: Find the change in y - coordinates

For the y - coordinates:
Comparing the y - coordinates of A(2,6) and X(3,1), the change in y is \(1 - 6=- 5\).
We can check with other corresponding vertices. For B(3, - 1) and Y(4, - 6), the change in x is \(4 - 3 = 1\) and the change in y is \(-6-(-1)=-5\). For C(-2,5) and Z(-1,0), the change in x is \(-1-(-2)=1\) and the change in y is \(0 - 5=-5\).

Answer:

You can translate each vertex of \(\triangle ABC\) 1 unit to the right and 5 units down to create \(\triangle XYZ\).