Chapter 6.8, Problem 2CYU

To determine

To find: The new vertices of the given figure after a dilation by the scale factor $k=\frac{1}{4}$ .

Answer to Problem 2CYU

New coordinates after dilating the given figure by given figure be

  $P\text{`}(\frac{1}{4},\frac{3}{4}),\text{T`}(\frac{5}{4},-\frac{1}{4}),\text{U`}\left(\frac{3}{2},\frac{3}{2}\right),\text{S`}(2,\frac{1}{2})$

Explanation of Solution

Given information: 

Given the following figure with vertices,

  $P\left(1,3\right),T\left(5,-1\right),\text{U}\left(6,6\right),S(8,2)$

  

Concept used:

To get the new coordinates of each vertex, each given original x and y coordinate will be multiplied by given scale factor $k=\frac{1}{4}$ .

Calculation:

Coordinate of imaged vertex:

  $\begin{array}{l}P`=\left(1\times \frac{1}{4},3\times \frac{1}{4}\right)=(\frac{1}{4},\frac{3}{4})\\ T`=\left(5\times \frac{1}{4},-1\times \frac{1}{4}\right)=(\frac{5}{4},-\frac{1}{4})\\ U`=\left(6\times \frac{1}{4},6\times \frac{1}{4}\right)=(\frac{3}{2},\frac{3}{2})\\ S`=\left(8\times \frac{1}{4},2\times \frac{1}{4}\right)=(2,\frac{1}{4})\end{array}$

So, new corresponding vertices are: $P\text{`}(\frac{1}{4},\frac{3}{4}),\text{T`}(\frac{5}{4},-\frac{1}{4}),\text{U`}\left(\frac{3}{2},\frac{3}{2}\right),\text{S`}(2,\frac{1}{2})$ .