Answer:
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 \(m=\frac{y_2-y_1}{x_2-x_1}\)
The slope of AB is :
\(m=\frac{8-2}{3-2}\)
\(m=\frac{6}{1}\)
\(m=6\)
Line AB is dilated by a scale factor of 3.5.
The length of AB by distance formula,
Distance formula, \(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)
\(d = \sqrt{(3 - 2)^2 + (8 - 2)^2}\)
\(d = \sqrt{(1)^2 + (6)^2}\)
\(d = \sqrt{1+36}\)
\(d = \sqrt{37}\)
The length of A'B' is :
\(d' =3.5\times \sqrt{37}\)
\(d' =3.5\sqrt{37}\)
Therefore, The slope is m=6 and length of line is
\(d' =3.5\sqrt{37}\)
Hence, Option C is correct.
