Question

critical thinking the coordinate notation shows how the coordinates of a figure are related to the coordinates of its image after transformations. $(x,y)\to(2x + 4,2y - 3)$ what are the transformations?

Explanation:

Step1: Analyze the \(x\) - coordinate transformation

For the \(x\) - coordinate, we have \(x\to2x + 4\).
The factor of \(2\) in front of \(x\) represents a horizontal stretch by a factor of \(2\). The addition of \(4\) to \(2x\) represents a horizontal translation (shift) of \(4\) units to the right.

Step2: Analyze the \(y\) - coordinate transformation

For the \(y\) - coordinate, we have \(y\to2y-3\).
The factor of \(2\) in front of \(y\) represents a vertical stretch by a factor of \(2\). The subtraction of \(3\) from \(2y\) represents a vertical translation (shift) of \(3\) units down.

Answer:

A horizontal stretch by a factor of \(2\), a horizontal translation \(4\) units to the right, a vertical stretch by a factor of \(2\), and a vertical translation \(3\) units down.