Question

(5, 8) → (8, -5)

Explanation:

Step1: Analyze the transformation of coordinates

Given the point \((5, 8)\) transforms to \((8, -5)\). Let's denote the original coordinates as \((x, y)=(5, 8)\) and the transformed coordinates as \((x', y')=(8, -5)\).
We can observe that \(x' = y\) (since \(8 = 8\) which is the \(y\)-coordinate of the original point) and \(y'=-x\) (since \(- 5=-5\) which is the negative of the \(x\)-coordinate of the original point). So the transformation rule is \((x,y)\to(y, - x)\).

Step2: Identify the type of transformation

This type of transformation is a rotation. The general rule for a rotation of \(90^{\circ}\) counter - clockwise about the origin is \((x,y)\to(-y,x)\) and for a rotation of \(90^{\circ}\) clockwise about the origin is \((x,y)\to(y, - x)\). Since our transformation follows \((x,y)\to(y, - x)\), it is a \(90^{\circ}\) clockwise rotation about the origin.

Answer:

The transformation from \((5, 8)\) to \((8, - 5)\) is a \(90^{\circ}\) clockwise rotation about the origin, following the rule \((x,y)\to(y, - x)\)