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=(d-b)/(c-a)`

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

`\begin{gathered} m=(-4-(-7))/(11-6) \\ m=(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} (-11)/(-2)=5.5 \\ (16.5)/(3)=5.5 \end{gathered}`

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