Question

the vertices of $\triangle abc$ are $a(-6, -7)$, $b(-3, -10)$, and $c(-5, 2)$. find the vertices of $\triangle abc$ given the translation rule below.
$(x, y) \to (x - 2, y - 7)$
\textbf{a} $a(-8, -14)$, $b(-5, -17)$, $c(-7, -5)$
\textbf{b} $a(-7, -17)$, $b(-4, -8)$, $c(-7, -5)$
\textbf{c} $a(-8, -17)$, $b(-5, -14)$, $c(-5, -5)$
\textbf{d} $a(5, -14)$, $b(-5, -14)$, $c(-7, -5)$

Explanation:

Step1: Translate point $A$

$A(-6,-7) \to (-6-2, -7-7) = (-8,-14)$

Step2: Translate point $B$

$B(-3,-10) \to (-3-2, -10-7) = (-5,-17)$

Step3: Translate point $C$

$C(-5,2) \to (-5-2, 2-7) = (-7,-5)$

Answer:

a. $A'(-8,-14)$, $B'(-5,-17)$, $C'(-7,-5)$