Question

triangle abc is translated according to the rule $(x,y)\to(x + 2,y - 8)$. if the coordinates of the pre - image of point b are $(4,-5)$, what are the coordinates of b? $(2,3)$ $(1,-9)$ $(-3,-4)$ $(6,-13)$

Explanation:

Step1: Calculate the x - coordinate of \( B'\)

Given the translation rule \((x,y)\to(x + 2,y-8)\) and the pre - image \(B=(4,-5)\). For the x - coordinate, use the formula \(x'=x + 2\). Substitute \(x = 4\) into the formula: \(x'=4+2=6\).

Step2: Calculate the y - coordinate of \(B'\)

For the y - coordinate, use the formula \(y'=y - 8\). Substitute \(y=-5\) into the formula: \(y'=-5-8=-13\).

Answer:

\((6,-13)\) (the fourth option)