Question

Question 19: Given are line m and point P not on m. What can be the image of m under a dilation with the center P?

Answer 1

• B. a line parallel to m

Step-by-step explanation:

Imagine two points S with coordinates (a,b) and T with coordinates (c,d) on the line m.

• The slope of the line m is (d - b) / (c -a)

For your convenience choose the point P as the center of your coordinate system.

Then, when you dilate the line m by a factor K, the images of the points S and T, S' and T', will have coordinates (K × a, K × b) and (K × c, K × d), respectively.

Thus, the slope of the image of the line m, to which the segment S'T' belong, is:

• {K × d - K × b] / [K × c - K × a] = [ K (d-b) ] / [ K (c - a) ] = (d - b) / (c - a)

Hence, the slope of the line m and its image are equal,which means that they are parallel.