Question

Triangle WXY has coordinates W(1, 5), X(1, 1), and Y(5, 1). Which of the following sets of points represents a dilation of triangle WXY?

A.
W'(1, 9); X'(1, 1); Y'(5, 1)
B.
W'(2, 10), X'(2, 2), Y'(10, 2)
C.
W'(2, 6), X'(2, 2), Y'(10, 2)
D.
W'(2, 10), X'(6, 2); Y'(10, 2)

Answer 1

A dilation of a figure with a scale factor of k, among other things, increases/decreases the size of the figure by a factor of k.

The vertex of the dilated figure is increased/decreased by a factor of k. Thus, given a point (x, y) in the coordinate plane which is dilated by a scale factor of k, the new point after dilation is given by k(x, y).

From the given options it can be seen that all the coordinates of the vertices of triangle WXY are multiplied by a factor of 2 in option B, hence a dilation with a scale factor of 2.

Therefore, the sets of points that represents a dilation of triangle WXY are W'(2, 10), X'(2, 2), Y'(10, 2) (option B).