Question

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

Explanation:

Step1: Determine the rotation rule

When a point \((x,y)\) is rotated \(- 90^{\circ}\) (which is equivalent to \(270^{\circ}\) clockwise) about the origin, the transformation rule is \((x,y)\to(y, - x)\).

Step2: Apply the rule to each vertex

• For point \(R(-7,7)\):

Using the rule \((x,y)\to(y, - x)\), we substitute \(x=-7\) and \(y = 7\).
The new coordinates are \((7,7)\).

• For point \(A(-1,7)\):

Substitute \(x=-1\) and \(y = 7\) into the rule \((x,y)\to(y, - x)\).
The new coordinates are \((7,1)\).

• For point \(M(-5,4)\):

Substitute \(x=-5\) and \(y = 4\) into the rule \((x,y)\to(y, - x)\).
The new coordinates are \((4,5)\).

• For point \(T(-5,1)\):

Substitute \(x=-5\) and \(y = 1\) into the rule \((x,y)\to(y, - x)\).
The new coordinates are \((1,5)\).

Step3: Plot the new points

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:

Plot the points \((7,7)\), \((7,1)\), \((4,5)\) and \((1,5)\) and connect them.