Question

use the scale factor to write the ordered pairs after the dilation. 13. a(4,4), b(8, 12), and k = ¾ 14. a(0, 0), b(-3, 2), and k = 5

Explanation:

Step1: Recall dilation formula

For a point $(x,y)$ dilated by a scale - factor $k$, the new point $(x',y')$ is given by $(x',y')=(k\cdot x,k\cdot y)$.

Step2: Find new coordinates for problem 13

For point A(4,4) with $k = \frac{3}{4}$, $x'=\frac{3}{4}\times4 = 3$ and $y'=\frac{3}{4}\times4 = 3$, so $A'(3,3)$.
For point B(8,12) with $k=\frac{3}{4}$, $x'=\frac{3}{4}\times8 = 6$ and $y'=\frac{3}{4}\times12 = 9$, so $B'(6,9)$.

Step3: Find new coordinates for problem 14

For point A(0,0) with $k = 5$, $x'=5\times0 = 0$ and $y'=5\times0 = 0$, so $A'(0,0)$.
For point B(-3,2) with $k = 5$, $x'=5\times(-3)=-15$ and $y'=5\times2 = 10$, so $B'(-15,10)$.

Answer:

1. $A'(3,3), B'(6,9)$
2. $A'(0,0), B'(-15,10)$