Question

ABC is dilated by a scale factor of 3 with the origin as the center of dilation to form A’B’C’. The slope of AB is -1.2. The length of AB is p units, the length of AC is q units, and the length of BC is r units.

The slope of A' B' is _________. The length of A'C' is _________ units.

a) 3.6; 3p
b) -3.6; 3q
c) -1.2; pr
d) 1.2; 3r

Answer 1

The slope of A'B' after dilation is -1.2, and the length of A'C' becomes 3q units because of the scale factor of 3.

Step-by-step explanation:

When a figure is dilated with the origin as the center of dilation, the slopes of the lines do not change because dilation is a similarity transformation. Thus, the slope of A'B' remains the same as the slope of AB, which is -1.2.

The lengths of the sides of the triangle, however, scale up by the factor of the dilation. Since the scale factor is 3, the length of A'C' will be three times the original length of AC. Therefore, the length of A'C' is 3q units.