Question

Triangle XYZ has vertices in the standard (x,y) coordinate plane at X(-3,-5), Y(4,-1), and Z(-2,6). A translation of triangle XYZ is a second triangle, XYZ, with vertices X(6,-10), Y(13,-6), and Z(a,b).

Answer 1

To translate triangle XYZ to triangle XYZ, subtract the coordinates of point X and add the translation vector to find the coordinates of point Z in the new triangle XYZ.

Step-by-step explanation:

To translate triangle XYZ to triangle XYZ, we need to find the coordinates of point Z in the new triangle. Let's start by finding the translation vector. The translation vector can be found by subtracting the coordinates of point X in both triangles. In this case, the translation vector is (6 - (-3), -10 - (-5)), which simplifies to (9, -5). To find the coordinates of point Z in the new triangle, we can add the translation vector to the coordinates of point Z in the original triangle. Given that point Z in the original triangle has coordinates (-2, 6), adding the translation vector gives us (9 + (-2), -5 + 6), which simplifies to (7, 1). Therefore, the coordinates of point Z in the new triangle XYZ are (a, b) = (7, 1).