Question

graph the image of trapezoid rstu after a rotation 180° counterclockwise around the origin.

Explanation:

Step1: Find the coordinates of the original trapezoid

From the graph, we can get the coordinates of the vertices of trapezoid \(RSTU\) as \(R(-1,4)\), \(S(-1,10)\), \(T(3,9)\), \(U(3,4)\).

Step2: Apply the rotation rule

The rule for a \(180^{\circ}\) counter - clockwise rotation around the origin is \((x,y)\to(-x,-y)\).
For point \(R(-1,4)\):
\((-1,4)\to(1, - 4)\)
For point \(S(-1,10)\):
\((-1,10)\to(1,-10)\)
For point \(T(3,9)\):
\((3,9)\to(-3,-9)\)
For point \(U(3,4)\):
\((3,4)\to(-3,-4)\)

Step3: Plot the new points

Plot the points \((1, - 4)\), \((1,-10)\), \((-3,-9)\), \((-3,-4)\) on the coordinate plane and connect them to form the image of the trapezoid after rotation.

Answer:

Plot the points \((1, - 4)\), \((1,-10)\), \((-3,-9)\), \((-3,-4)\) and connect them.