Question

Triangle XYZ is translated 4 units up and 3 units left to yield ΔX′Y′Z′. What is the distance between any two corresponding points on ΔXYZ and ΔX′Y′Z′?

Answer 1

see attachment

if you move the whole triangle up 4 units and to the left 3 units without rotating or dialating it, then each point should move up 4 units and 3 units to the left

find the distance between the first point and the translated point

if we draw out the path, we can see that the path makes 2 legs of a right triangle. the distance between the start and end is the hypotonuse

the 2 legs are length 3 and 4

by the pythagorean theorem, d²=3²+4²

d²=9+16

d²=25

d=5

so the distance between any 2 points on the original triangle and the translated triangle is 5 units