Triangle XYZ

Question

X
Y
Z
is translated down 4 units and to the left 8 units. The length of side XY
X
Y
is 10 units. What is the length of side X′Y′
X
′
Y
′
?

Answer 1

The length of a side of a triangle does not change when the triangle is translated. Translation preserves the shape and size of the triangle, simply moving it to a different location in the coordinate plane.

In this case, since triangle $XYZ$ is translated down 4 units and to the left 8 units, the length of side $XY$ will remain the same after the translation.

Given that the length of side $XY$ is 10 units, the length of side $X^{\prime }{Y}^{\prime }$ (the translated side) will also be:

$$\text{Length of }{X}^{\prime }{Y}^{\prime }=10\text{ units}$$

So, the length of side $X^{\prime }{Y}^{\prime }$ is 10 units.