XYZ has vertices X(-2, 2), Y(3, 2), and Z(-5, -6). What are the new coordinates if it's translated 2 units up and 4 units to the right, then dilated by a scale factor of 2?
Question
XYZ has vertices X(-2, 2), Y(3, 2), and Z(-5, -6). What are the new coordinates if it's translated 2 units up and 4 units to the right, then dilated by a scale factor of 2?
Solution
Step 1: Translation The translation of a point (x, y) by 2 units up and 4 units to the right is given by (x+4, y+2).
So, the new coordinates after translation are: X' = X(-2+4, 2+2) = X(2, 4) Y' = Y(3+4, 2+2) = Y(7, 4) Z' = Z(-5+4, -6+2) = Z(-1, -4)
Step 2: Dilation The dilation of a point (x, y) by a scale factor of 2 is given by (2x, 2y).
So, the new coordinates after dilation are: X'' = X'(22, 24) = X'(4, 8) Y'' = Y'(27, 24) = Y'(14, 8) Z'' = Z'(2*-1, 2*-4) = Z'(-2, -8)
So, the new coordinates of the vertices X, Y, and Z after the translation and dilation are X(4, 8), Y(14, 8), and Z(-2, -8) respectively.
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