Chapter 6.8, Problem 25STP

To determine

To calculate : Number representing the scale factor used to dilate quadrilateral PQRS to quadrilateral P`Q`R`S`

Answer to Problem 25STP

C. $\frac{1}{2}$

Explanation of Solution

Given information : Coordinates of

  $P(x,y)=(-4,2)$ and $P^{\prime }(x,y)=(-2,1)$

  $Q(x,y)=(0,2)$ and $Q^{\prime }(x,y)=(0,1)$

  $R(x,y)=(2,0)$ and $R^{\prime }(x,y)=(1,0)$

  $S(x,y)=(-2,-2)$ and $S^{\prime }(x,y)=(-1,-1)$

Formula used - new coordinates can be found out by multiplication of old coordinates with scale factor.i.e. scale factor $=\frac{n\text{ ev coordinates }}{\text{ old coordinates }}$

Calculation:

scale factor${}_p=\frac{{\text{new coordinates}}_p}{{\text{old coordinates}}_p}=\frac{(-2,1)}{(-4,2)}=\frac{1}{2}$

scale factor${}_Q=\frac{{\text{new coordinates}}_Q}{{\text{old coordinates}}_Q}=\frac{(0,1)}{(0,2)}=\frac{1}{2}$

scale factor${}_R=\frac{{\text{new coordinates}}_R}{{\text{old coordinates}}_R}=\frac{(1,0)}{(2,0)}=\frac{1}{2}$

scale factor${}_s=\frac{{\text{new coordinates}}_s}{{\text{old coordinates}}_s}=\frac{(-1,-1)}{(-2,-2)}=\frac{1}{2}$