Question

after the point y(-4, -9) is translated along the vector < -2, 8 > the image will be located at ( , )

Explanation:

Step1: Recall translation rule

To translate a point \((x, y)\) along a vector \(\langle a, b
angle\), we add \(a\) to the \(x\)-coordinate and \(b\) to the \(y\)-coordinate. So the new coordinates \((x', y')\) are given by \(x' = x + a\) and \(y' = y + b\).

Step2: Identify values

Here, the point is \(Y(-4, -9)\) and the vector is \(\langle -2, 8
angle\). So \(x = -4\), \(y = -9\), \(a = -2\), and \(b = 8\).

Step3: Calculate new x-coordinate

\(x' = -4 + (-2) = -6\)

Step4: Calculate new y-coordinate

\(y' = -9 + 8 = -1\)

Answer:

\((-6, -1)\)