The endpoints of line ab are a(2, 2) and b(3, 8). line ab is dilated by a scale factor of 3.5 with the origin as the center of dilation to give image line a'b' . what are the slope (m) and length of line ab? use the distance formula to you decide: . a. m=21, a'b'=3.5 √37
b. m=6, a'b'= √37
c. m=6, a'b'=3.5√37
d. m=21, a'b'=√37
e. m=6,a'b'=6√37

Option C -  m=6, A'B'=3.5√37

Step-by-step explanation:

Given : The endpoints of line AB are A(2, 2) and B(3, 8). Line AB is dilated by a scale factor of 3.5 with the origin as the center of dilation to give image line A'B' .

To find : What are the slope (m) and length of line AB?

Solution :

The slope of a line does not change.

Slope formula is

The slope of AB is :  

Line AB is dilated by a scale factor of 3.5.

The length of AB by distance formula,

Distance formula,

The length of A'B' is :

Therefore, The slope is m=6 and length of line is  

Hence, Option C is correct.