Chapter SR14, Problem 23P

Solution

The coordinates of the vertices of a polygon are given. Draw the polygon. Then find the coordinates of the vertices of the image after the specified dilation, and draw the image.

Coordinates after dilation $A\text{'}(1,1)$ , $B\text{'}(3,-1)$ , $C\text{'}(2,-3)$ and $D\text{'}(0,-3)$ .

Given:

(2,-2), (6, -2), (4,-6), (0,-6); dilate using a scale factor of $\frac{1}{2}$ .

Concept Used:

• The scale factor is k, so multiply every coordinates by k.
• Use (x, y) = (kx, ky) with each vertex.

Calculation:

The vertices of a polygon are (2,-2), (6, -2), (4,-6), (0,-6).

Let name the vertices −A(2,-2), B(6, -2), C(4,-6), D(0,-6).

The graph of given polygon is -

  

Scale factor of $k=\frac{1}{2}$ .

So multiply every coordinate by $\frac{1}{2}$ .

  $A(2,2)=A\text{'}(2\cdot \frac{1}{2},2\cdot \frac{1}{2})=A\text{'}(1,1)$

  $B(6,-2)=B\text{'}(6\cdot \frac{1}{2},-2\cdot \frac{1}{2})=B\text{'}(3,-1)$

  $C(4,-6)=C\text{'}(4\cdot \frac{1}{2},-6\cdot \frac{1}{2})=C\text{'}(2,-3)$

  $D(0,-6)=D\text{'}(0\cdot \frac{1}{2},-6\cdot \frac{1}{2})=D\text{'}(0,-3)$

Graphing the new vertices after dilation -