Chapter SR14, Problem 19P

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 $A\text{'}(3,9)$ , $B\text{'}(9,6)$ and $C\text{'}(6,15)$ .

Given:

(1, 3), (3, 2), (2, 5); dilate using a scale factor of 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 (1, 3), (3, 2), (2, 5).

Let name the vertices - A(1, 3), B(3, 2), C(2, 5).

The graph of given polygon is -

  

Scale factor of k=3.

So multiply every coordinate by 3.

  $A(1,3)=A\text{'}(1\cdot 3,3\cdot 3)=A\text{'}(3,9)$

  $B(3,2)=B\text{'}(3\cdot 3,2\cdot 3)=B\text{'}(9,6)$

  $C(2,5)=C\text{'}(2\cdot 3,5\cdot 3)=C\text{'}(6,15)$

Graphing the new vertices after dilation -