Question

quadrilateral team is rotated - 180° about the origin. draw the image of this rotation.

Explanation:

Step1: Find coordinates of original points

From the graph, the coordinates of the vertices of quadrilateral \(TEAM\) are \(T(3,-2)\), \(E(2,4)\), \(A(-2,3)\), \(M(6,7)\).

Step2: Apply the rotation rule

The rule for a rotation of \(- 180^{\circ}\) (which is the same as a rotation of \(180^{\circ}\)) about the origin is \((x,y)\to(-x,-y)\).
For point \(T(3,-2)\): \((3,-2)\to(-3,2)\)
For point \(E(2,4)\): \((2,4)\to(-2,-4)\)
For point \(A(-2,3)\): \((-2,3)\to(2,-3)\)
For point \(M(6,7)\): \((6,7)\to(-6,-7)\)

Step3: Plot the new points

Plot the points \(T'(-3,2)\), \(E'(-2,-4)\), \(A'(2,-3)\), \(M'(-6,-7)\) on the coordinate - plane and connect them to form the rotated quadrilateral.

Answer:

Plot the points \(T'(-3,2)\), \(E'(-2,-4)\), \(A'(2,-3)\), \(M'(-6,-7)\) and connect them.