triangle qrs is to be dilated using the rule $d_{p,\frac{3}{4}}$. what will be the distance from the center…

triangle qrs is to be dilated using the rule $d_{p,\frac{3}{4}}$. what will be the distance from the center of dilation, p, to the image s? 2 units 4 units 6 units 8 units

triangle qrs is to be dilated using the rule $d_{p,\frac{3}{4}}$. what will be the distance from the center of dilation, p, to the image s? 2 units 4 units 6 units 8 units

Answer

Explanation:

Step1: Recall dilation formula

The distance from the center of dilation $P$ to a point $S$ is $d(PS) = 8$ units. The rule of dilation is $D_{P,\frac{3}{4}}$, which means the scale - factor $k=\frac{3}{4}$. The distance from the center of dilation $P$ to the image $S'$ is given by $d(PS')=k\times d(PS)$.

Step2: Calculate the distance

Substitute $k = \frac{3}{4}$ and $d(PS)=8$ into the formula $d(PS')=k\times d(PS)$. So $d(PS')=\frac{3}{4}\times8$. $d(PS') = 6$ units.

Answer:

6 units