Chapter 6.8, Problem 1GP

To determine

To find: The new vertices of the given figure after dilation by the scale factor $\frac{1}{3}$ , also graph the figure.

Answer to Problem 1GP

New coordinates after dilating the figure with given vertices $\text{<msup><mo>R</mo><mo>′</mo></msup>}\left(-1,2\right),\text{<msup><mo>S</mo><mo>′</mo></msup>}\left(1,4\right),\text{<msup><mo>T</mo><mo>′</mo></msup>}(1,1)$

Explanation of Solution

Given information: Given the following vertices of a figure $R\left(-3,6\right),S\left(3,12\right)$ and $T(3,3)$ to be dilated by scale factor $\frac{1}{3}$ .

Concept used:

To get the new coordinates of each vertex, each given original x and y coordinate will be multiplied by given scale factor $\frac{1}{3}$ .

Calculation:

Coordinate of imaged vertex:

  $R^{\prime }=\left(-3\times \frac{1}{3},6\times \frac{1}{3}\right)=(-1,2)$ .

  $\begin{array}{l}{S}^{\prime }=\left(3\times \frac{1}{3},12\times \frac{1}{3}\right)=(1,4)\\ C^{\prime }=\left(3\times \frac{1}{3},3\times \frac{1}{3}\right)=(1,1)\end{array}$

Now, the graph is,

  

Therefore, new corresponding vertices are: $\text{<msup><mo>R</mo><mo>′</mo></msup>}\left(-1,2\right),\text{<msup><mo>S</mo><mo>′</mo></msup>}\left(1,4\right),\text{<msup><mo>T</mo><mo>′</mo></msup>}(1,1)$