Chapter SR14, Problem 21P

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 $A\text{'}(1,1)$ , $B\text{'}(2,1)$ , $C\text{'}(1,-1)$ and $D\text{'}(2,-1)$ .

Given:

(3, 3), (6, 3), (3, -3), (6, -3); dilate using a scale factor of $\frac{1}{3}$ .

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 (3, 3), (6, 3), (3, -3), (6, -3).

Let name the vertices − A(3, 3), B(6, 3), C(3, -3), D(6, -3)

The graph of given polygon is -

  

Scale factor of $k=\frac{1}{3}$ .

So multiply every coordinate by $\frac{1}{3}$ .

  $A(3,3)=A\text{'}(3\cdot \frac{1}{3},3\cdot \frac{1}{3})=A\text{'}(1,1)$

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

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

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

Graphing the new vertices after dilation -