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′ ?(1 point)
units
Since triangle XYZ is translated down 4 units and to the left 8 units, the coordinates of point X' is (-8, -4).
To find the length of side X'Y', we need to find the distance between point X' and Y'.
Since we know the length of side XY is 10 units, we can use the distance formula to find the length of side X'Y':
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Plugging in the coordinates of X' (-8, -4) and Y' (x, y), we have:
d = sqrt((x - (-8))^2 + (y - (-4))^2)
Since the translation is only in the x and y direction, the x-coordinate of Y' remains the same, so we have:
d = sqrt((x - (-8))^2 + (y - (-4))^2)
We can simplify this by removing the squares:
d = sqrt((x + 8)^2 + (y + 4)^2)
Since we don't know the coordinates of point Y', we can't find the exact length of side X'Y'. However, we can state that the length of side X'Y' is the same as the length of side XY, which is 10 units. Therefore, the length of side X'Y' is 10 units.