Question

AABC is dilated by a scale factor of 3 with the origin as the center of dilation to form ABC. 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 ( 1/3.6 ). The length of A'C' is ( 3p ) units.

a) ( 1/3.6 ), ( 3q )
b) ( -1.2 ), ( 3r )
c) ( -1.2 ), ( 3p )
d) ( 1/3.6 ), ( 3p )

Answer 1

The slope of A' B' is (1/3.6) and the length of A' C' is (3p).

Step-by-step explanation:

To find the slope of A' B', we can use the fact that the scale factor of the dilation is 3. This means that the lengths of corresponding sides are multiplied by 3. Since AB has a slope of -1.2, A' B' will have a slope of (1/3.6) because (1/3.6)(-1.2) = -0.333, which is approximately equal to (1/3.6).

To find the length of A' C', we can also use the scale factor of 3. Since AC has a length of q, A' C' will have a length of 3q because 3(q) = 3q. Therefore, the correct answer is (1/3.6) for the slope of A' B' and (3p) for the length of A' C', so the option is d) (1/3.6), (3p).