Question

the image point of a after a translation right 1 unit and down 3 units is the point ( b(5,-3) ). determine the coordinates of the pre - image point a.

Explanation:

Step1: Analyze the translation rules

A translation right \(1\) unit means \(x\) - coordinate of pre - image \(x\) becomes \(x + 1\) in the image. A translation down \(3\) units means \(y\) - coordinate of pre - image \(y\) becomes \(y-3\) in the image. Let the coordinates of point \(A\) be \((x,y)\). Then the coordinates of point \(B\) (image) are \((x + 1,y-3)\).

Step2: Set up equations

We know that \(x + 1=5\) and \(y-3=-3\).
For the \(x\) - coordinate:
Solve \(x + 1=5\) for \(x\). Subtract \(1\) from both sides of the equation: \(x=5 - 1\).
For the \(y\) - coordinate:
Solve \(y-3=-3\) for \(y\). Add \(3\) to both sides of the equation: \(y=-3 + 3\).

Answer:

The coordinates of point \(A\) are \((4,0)\)