Question

part a: describe the transformation that maps \\( \triangle j k l \\) to \\( \triangle p q r \\).
part b: algebraically represent the transformation needed to map \\( \triangle j k l \\) to \\( \triangle p q r \\).

Explanation:

Part A:

Step1: Analyze the transformation type

By observing the orientation and position of the triangles, we can see that it is a rotation.

Step2: Determine the rotation direction and angle

Since the figure is rotated counter - clockwise around the origin \(O\) (as the center of rotation) by \(90^{\circ}\).

Part B:

Step1: Recall the rotation formula

For a point \((x,y)\) rotated counter - clockwise by \(90^{\circ}\) around the origin, the transformation formula is \((x,y)\to(-y,x)\)

Answer:

Part A:

The transformation that maps \(\triangle JKL\) to \(\triangle PQR\) is a \(90^{\circ}\) counter - clockwise rotation about the origin.

Part B:

The algebraic representation of the transformation is \((x,y)\to(-y,x)\)