Chapter 6.8, Problem 1CYU

To determine

To find: The new vertices of the given figure after dilation by the scale factor $k=\frac{1}{2}$ .

Answer to Problem 1CYU

New coordinates after dilating the given figure by given figure be $\text{A`}\left(-1,\frac{1}{2}\right),\text{B`}\left(\frac{1}{2},1\right),\text{C`}(\frac{3}{2},-1)$ .

Explanation of Solution

Given information: Given the following figure with vertices,

  $\text{A}\left(-2,1\right),\text{B}\left(1,2\right),\text{C}(3,-2)$

  

Concept used:

To get the new coordinates of each vertex, each given original x and y coordinate will be multiplied by given scale factor $k=\frac{1}{2}$ .

Calculation:

Coordinate of imaged vertex $A`=\left(-2\times \frac{1}{2},1\times \frac{1}{2}\right)=\left(-1,\frac{1}{2}\right)$

  $\begin{array}{l}B`=\left(1\times \frac{1}{2},2\times \frac{1}{2}\right)=\left(\frac{1}{2},1\right)\\ C`=\left(3\times \frac{1}{2},-2\times \frac{1}{2}\right)=\left(\frac{3}{2},-1\right)\end{array}$

So, new corresponding vertices are $\text{A`}\left(-1,\frac{1}{2}\right),\text{B`}\left(\frac{1}{2},1\right),\text{C`}(\frac{3}{2},-1)$ .