Question

the image of the point (-1, -8) under a translation is (0, -11). find the coordinates of the image of the point (-4, -1) under the same translation.

Explanation:

Step1: Find the translation rule

Let the translation rule be \((x,y)\to(x + a,y + b)\).
Given \((-1,-8)\to(0,-11)\), then \(-1+a = 0\) and \(-8 + b=-11\).
From \(-1+a = 0\), we get \(a=1\).
From \(-8 + b=-11\), we get \(b=-3\). So the translation rule is \((x,y)\to(x + 1,y-3)\).

Step2: Apply the translation rule to the point \((-4,-1)\)

For the point \((-4,-1)\), when \(x=-4\) and \(y = -1\).
The \(x\)-coordinate of the image: \(x'=-4 + 1=-3\).
The \(y\)-coordinate of the image: \(y'=-1-3=-4\).

Answer:

\((-3,-4)\)