Question

13 a) (x,y)→(x + 2,y + 4) b) (-2 4) 15. p(1, -2) is the image of p after a translation along the vector (-8, 0). what are the coordinates of p? (9, -2) ©gina wilson (all things algebra®, llc). 2015 - 2018

Explanation:

Step1: Recall translation formula

The translation formula is $(x',y')=(x + a,y + b)$, where $(x,y)$ are the original - coordinates, $(x',y')$ are the image - coordinates, and $(a,b)$ is the translation vector.

Step2: Identify given values

We are given that $(x',y')=(1, - 2)$ and $(a,b)=(-8,0)$.

Step3: Solve for original x - coordinate

Using the formula $x'=x + a$, we substitute the values: $1=x+( - 8)$. Rearranging the equation gives $x=x'-a$. So, $x = 1-(-8)=1 + 8=9$.

Step4: Solve for original y - coordinate

Using the formula $y'=y + b$, we substitute the values: $-2=y + 0$. So, $y=-2$.

Answer:

$(9,-2)$