Question

13 a) $(x,y)\to(x + 2,y + 4)$ b) $\begin{pmatrix}-2\\-4end{pmatrix}$ 15. $p(1,-2)$ is the image of $p$ after a translation along the vector $langle-8,0
angle$. what are the coordinates of $p$? $(9,-2)$ © gina wilson (all things algebra®, llc), 2015 - 2018

Explanation:

Step1: Recall translation formula

For a translation along the vector $\langle a,b
angle$, if a point $P(x,y)$ is translated to $P'(x',y')$, then $x'=x + a$ and $y'=y + b$. Here $a=-8$ and $b = 0$, and $x'=1,y'=-2$.

Step2: Solve for $x$

We know that $x'=x + a$. Substituting $x' = 1$ and $a=-8$ into the formula $x'=x + a$, we get $1=x-8$. Solving for $x$ gives $x=1 + 8=9$.

Step3: Solve for $y$

We know that $y'=y + b$. Substituting $y'=-2$ and $b = 0$ into the formula $y'=y + b$, we get $-2=y+0$, so $y=-2$.

Answer:

$(9,-2)$