Question

a) what is the slope of a line that passes through (6,-7) and (11,-4)?b)what is the scale factor for the dilation with points A (-2,3) and A's (-11,16.5)?

Answer 1

a) The slope of the line that passes through two points (a,b), (c,d) is given by

$m=\frac{d-b}{c-a}$

Replacing (6,-7),(11,-4)

$\begin{gathered} m=\frac{-4-(-7)}{11-6} \\ m=\frac{3}{5} \end{gathered}$

Then, the slope is 3/5.

The dilation can be obtained by multiplying both coordinates by the same factor. Since

$\begin{gathered} \frac{-11}{-2}=5.5 \\ \frac{16.5}{3}=5.5 \end{gathered}$

then (-11,16.5) = 5.5(-2,3) and the scale factor is 5.5