Chapter 6.8, Problem 24HP

To determine

To find: the coordinates of that vertex after both dilations.

Answer to Problem 24HP

The coordinates is $\left(3,6\right)$ .

Explanation of Solution

Given information:

A triangle has one vertex at point $\left(3,6\right)$ . It is dilated with a center at the origin by a scale factor of 3. The resulting image is then dilated with a scale factor of $\frac{1}{3}$

Calculation:

Triangle has one vertex at $\left(3,6\right)$ .

Scale factor is 3.

Image is dilated with scale factor of $\frac{1}{3}$

Consider the vertex $\left(3,6\right)$ .

$\left(3,6\right)$ for scale factor 3 vertex $\left(9,18\right)$ .

Then scale factor is $\frac{1}{3}$ , so vertex is $\left(3,6\right)$ .

Result is same.

There is no change in the vertex.

Hence, the new coordinates is $\left(3,6\right)$ .