Question

the parallelogram will be rotated 90° clockwise about the origin.
draw the rotated parallelogram by clicking on each of its vertices.
the parallelogram will turn blue when complete.

Explanation:

Step1: Identify Original Vertices

First, find the coordinates of the original parallelogram's vertices. From the graph, the vertices (let's assume) are: \( A(-1, 7) \), \( B(0, 5) \), \( C(0, 0) \), \( D(-1, 2) \) (by looking at the grid points).

Step2: Apply 90° Clockwise Rotation Rule

The rule for rotating a point \((x, y)\) 90° clockwise about the origin is \((x, y) \to (y, -x)\).

• For \( A(-1, 7) \): New coordinates \((7, 1)\) (since \( x=-1, y=7 \); \( y=7, -x = 1 \))
• For \( B(0, 5) \): New coordinates \((5, 0)\) ( \( x=0, y=5 \); \( y=5, -x = 0 \))
• For \( C(0, 0) \): New coordinates \((0, 0)\) ( \( x=0, y=0 \); \( y=0, -x = 0 \))
• For \( D(-1, 2) \): New coordinates \((2, 1)\) ( \( x=-1, y=2 \); \( y=2, -x = 1 \))

Step3: Plot Rotated Vertices

Plot the points \((7, 1)\), \((5, 0)\), \((0, 0)\), \((2, 1)\) on the grid. Connect them to form the rotated parallelogram. (Note: The actual plotting is done by clicking on these vertices in the interactive graph, but the key is calculating the rotated coordinates.)

Answer:

To draw the rotated parallelogram, plot the vertices obtained by rotating each original vertex \((x, y)\) 90° clockwise (using \((y, -x)\)): \((7, 1)\), \((5, 0)\), \((0, 0)\), \((2, 1)\) and connect them.