Question

question
the image of the point $(-8,-9)$ under a translation is $(-11,-14)$. find the coordinates of the image of the point $(0,-6)$ under the same translation.
answer

Explanation:

Step1: Find the translation rule

The translation rule is \((x,y)\to(x + a,y + b)\).
For the point \((-8,-9)\) and its image \((-11,-14)\), we have \(-8+a=-11\) and \(-9 + b=-14\).
Solving \(-8+a=-11\) gives \(a=-11+8=-3\).
Solving \(-9 + b=-14\) gives \(b=-14 + 9=-5\).
So the translation rule is \((x,y)\to(x-3,y - 5)\).

Step2: Apply the translation rule to the point \((0,-6)\)

For \(x = 0\) and \(y=-6\), using the rule \(x'=x-3\) and \(y'=y - 5\).
\(x'=0-3=-3\), \(y'=-6-5=-11\).

Answer:

\((-3,-11)\)