Question

type the coordinates of the images p, q, and r for each of the following points under the translation defined by (x,y)→(x+7,y−8)
a) p(0,0) b) q(−5,2) c) r(−8,−8)

a) p(0,0)→p (7, -8) (type an ordered pair.)
b) q(−5,2)→q \square (type an ordered pair.)

Explanation:

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

For the translation \((x,y)\to(x + 7,y-8)\), when \(x=-5\), the new \(x\) - coordinate is \(x'=-5 + 7\).
\(x'=-5+7 = 2\)

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

When \(y = 2\), the new \(y\) - coordinate is \(y'=2-8\).
\(y'=2 - 8=-6\)

Answer:

\((2,-6)\)