Question

quadrilateral tram is rotated $-90^{circ}$ about the origin. draw the image of this rotation.

Explanation:

Step1: Determine the rotation rule

A rotation of \(-90^{\circ}\) about the origin has the rule \((x,y)\to(y, -x)\).

Step2: Apply the rule to each vertex

• For \(R(-7,7)\): \((-7,7)\to(7,7)\)
• For \(A(-1,7)\): \((-1,7)\to(7,1)\)
• For \(M(-5,4)\): \((-5,4)\to(4,5)\)
• For \(T(-5,1)\): \((-5,1)\to(1,5)\)

Step3: Plot the new vertices

Plot the points \((7,7)\), \((7,1)\), \((4,5)\), and \((1,5)\) on the coordinate plane and connect them to form the rotated quadrilateral.

Answer:

The image of quadrilateral \(TRAM\) after a \(-90^{\circ}\) rotation about the origin is formed by the vertices \((7,7)\), \((7,1)\), \((4,5)\), and \((1,5)\).