4. Triangle XYZ is translated down 4 units and to the left 8 units. The length of side XY is 10 units. What is the length of side X′Y′?
Since triangle XYZ is translated down 4 units, this means that all the points of triangle XYZ are shifted downward by 4 units. Therefore, the coordinates of points X, Y, and Z are now (x, y-4), (x-8, y-4), and (x, y-4), respectively.
The length of side XY is given as 10 units, which means that the distance between points X and Y is 10 units. Using the distance formula, we can calculate the length of side XY:
√((x - (x-8))^2 + ((y-4) - (y-4))^2) = 10
Simplifying the equation, we have:
√(8^2) = 10
Solving for 8^2, we get:
8^2 = 10^2
64 = 100
Since this is not a valid equation, it means that there is an error in the given information. Without the correct coordinates of point Y', we cannot determine the length of side X'Y'.