To determine the pre-image, we need to undo the translation that was applied to the original quadrilateral.
The original quadrilateral had vertices P', Q', R', and S', and we can express their coordinates as follows:
P' = (xP, yP)
Q' = (xQ, yQ)
R' = (xR, yR)
S' = (xS, yS)
Since the quadrilateral was translated left by two units and up by five units, we can express the new coordinates as follows:
P = P' + (-2, 5) = (xP - 2, yP + 5)
Q = Q' + (-2, 5) = (xQ - 2, yQ + 5)
R = R' + (-2, 5) = (xR - 2, yR + 5)
S = S' + (-2, 5) = (xS - 2, yS + 5)
Using the given coordinates of the image vertices, we can set up four equations for xP, yP, xQ, yQ, xR, yR, xS, and yS:
xP - 2 = 1
yP + 5 = -5
xQ - 2 = 4
yQ + 5 = 3
xR - 2 = -2
yR + 5 = 7
xS - 2 = -3
yS + 5 = 1
Solving these equations, we get:
xP = 3, yP = -10
xQ = 6, yQ = -2
xR = 0, yR = 2
xS = -1, yS = -4
Therefore, the pre-image quadrilateral has vertices at P'(3, -10), Q'(6, -2), R'(0, 2), and S'(-1, -4).
A quadrilateral has been translated two units to the left and five units up. Its image vertices are P(1,-5), Q(4, 3), R(-2, 7), S(-3, 1): Determine the coordinates of the pre-image. Explain your thinking.
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