Question

ΔXYZ 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

For a better understanding of the solution provided here, please go through the diagram in the file that has been attached. The diagram is to a large extent self explanatory.

As can be seen from the diagram, ΔXYZ is translated 4 units up and 3 units left to yield ΔX′Y′Z′. This means that each point in ΔXYZ is moved up 4 units and moved left 3 units.

Let us take the case of the points Z and Z'. The distance of Z' from Z can be calculated by applying the Pythagoras' Theorem in the right triangle ZPZ' as:

$ZZ'=\sqrt{4^2+3^2}=5$

Thus, we can conclude that the the distance between any two corresponding points on ΔXYZ and ΔX′Y′Z′  is 5 units.