Chapter SR14, Problem 20P

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 $A\text{'}(3,12)$ , $B\text{'}(3,6)$ , $C\text{'}(9,12)$ and $D\text{'}(9,6)$ .

Given:

(2, 8), (2, 4), (6, 8), (6, 4); dilate using a scale factor of $\frac{3}{2}$ .

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, 8), (2, 4), (6, 8), (6, 4).

Let name the vertices − A(2, 8), B(2, 4), C(6, 8), D(6, 4).

The graph of given polygon is -

  

Scale factor of $k=\frac{3}{2}$ .

So multiply every coordinate by $\frac{3}{2}$ .

  $A(2,8)=A\text{'}(2\cdot \frac{3}{2},8\cdot \frac{3}{2})=A\text{'}(3,12)$

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

  $C(6,8)=C\text{'}(6\cdot \frac{3}{2},8\cdot \frac{3}{2})=C\text{'}(9,12)$

  $D(6,4)=D\text{'}(6\cdot \frac{3}{2},4\cdot \frac{3}{2})=D\text{'}(9,6)$

Graphing the new vertices after dilation -