Question

triangle abc has vertices located at a(-3, 3), b(-2, 3) and c(-1, 2). triangle abc is the result of dilating triangle abc using point o(-5, 1) as the center of dilation and a scale - factor of 2. heres your sketch from the previous screen. what are the coordinates of triangle abc?

Explanation:

Step1: Recall dilation formula

For a point $(x,y)$ dilated about a center $(a,b)$ with a scale - factor $k$, the new point $(x',y')$ is given by $x'=a + k(x - a)$ and $y'=b + k(y - b)$. Here, assume the scale - factor $k = 2$ (not given in the problem but a common dilation factor, if not specified otherwise), and the center of dilation $O(-5,1)$.

Step2: Find coordinates of $A'$

For point $A(-3,3)$:
$x_{A'}= - 5+2(-3+5)=-5 + 2\times2=-5 + 4=-1$
$y_{A'}=1+2(3 - 1)=1+2\times2=1 + 4 = 5$
So, $A'(-1,5)$.

Step3: Find coordinates of $B'$

For point $B(-2,3)$:
$x_{B'}= - 5+2(-2 + 5)=-5+2\times3=-5 + 6 = 1$
$y_{B'}=1+2(3 - 1)=1+2\times2=1 + 4 = 5$
So, $B'(1,5)$.

Step4: Find coordinates of $C'$

For point $C(-1,2)$:
$x_{C'}= - 5+2(-1 + 5)=-5+2\times4=-5 + 8 = 3$
$y_{C'}=1+2(2 - 1)=1+2\times1=1 + 2 = 3$
So, $C'(3,3)$.

Answer:

$A'(-1,5)$
$B'(1,5)$
$C'(3,3)$