Triangle XYZ is translated down for units into the left eight units. The length of side xy is 10 units. What is the length side of X'Y'?
To find the length of side X'Y', we need to first determine the coordinates of the new point X' after the translation.
Let's assume the original coordinates of point X are (x1, y1).
After translating down 4 units, the new y-coordinate of X' will be y1 - 4.
After translating to the left 8 units, the new x-coordinate of X' will be x1 - 8.
Therefore, the coordinates of X' are (x1 - 8, y1 - 4).
Since we know that the length of side xy is 10 units, we can now use the distance formula to find the length of side X'Y'.
The distance formula is:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
In this case, x1 = x, y1 = y, x2 = x - 8, and y2 = y - 4.
Plugging in the values, we get:
Distance = √((x - (x - 8))^2 + (y - (y - 4))^2)
Distance = √(8^2 + 4^2)
Distance = √(64 + 16)
Distance = √80
Distance = 8√5
Therefore, the length of side X'Y' is 8√5 units.