Chapter 8.1, Problem 61SPR

To determine

To sketch: The graph from the points and verify that the dilation is a similarity transformation.

Answer to Problem 61SPR

By SAS similarity theorem triangles are similar.

Explanation of Solution

Given Information:

  $M\left(7,-4\right),N\left(5,-4\right),P\left(7,-1\right);Q\left(2,-8\right),R\left(6,-8\right),S\left(2,-2\right)$ .

Graph:

Consider the given points $M\left(7,-4\right),N\left(5,-4\right),P\left(7,-1\right);Q\left(2,-8\right),R\left(6,-8\right),S\left(2,-2\right)$ .

Now, draw the graph.

  

Interpretation:

From the figure there are two triangles $\Delta SQR\text{and}\Delta PMN$ .

Now,

  $\frac{SQ}{PM}=\frac{QR}{NM}=\frac{1}{2}$

And $\angle Q=m\angle M=90°$

Thus, the corresponding angles are congruent.

Thus, by SAS similarity theorem triangles are similar.