Question

the image point of a after a translation left 3 units and down 1 unit is the point b(-6,3). determine the coordinates of the pre - image point a.

Explanation:

Step1: Analyze the translation rule

A translation left \(3\) units means \(x\)-coordinate \(x\to x - 3\), and a translation down \(1\) unit means \(y\)-coordinate \(y\to y-1\). Let the coordinates of point \(A\) be \((x,y)\). Then the coordinates of point \(B\) are \((x - 3,y - 1)\).

Step2: Set up equations

We know that \(x-3=-6\) and \(y - 1=3\).
For \(x-3=-6\), add \(3\) to both sides: \(x=-6 + 3=-3\).
For \(y - 1=3\), add \(1\) to both sides: \(y=3 + 1=4\).

Answer:

\((-3,4)\)