Question

draw the size of the actual wall of the birdhouse by dilating the figure on the coordinate grid with a center of dilation at the origin and a scale factor of 2. use the polygon tool to plot the actual wall of the birdhouse.

Explanation:

Step1: Identify original vertices

First, find the coordinates of the original figure's vertices. From the grid:

• Top - left: \((0, 7)\)
• Top - right: \((4, 4)\)
• Bottom - right: \((4, 1)\)
• Bottom - left: \((2, 1)\)

Step2: Apply dilation (scale factor 2)

To dilate a point \((x, y)\) with center at the origin and scale factor \(k\), the new coordinates are \((kx, ky)\).

• For \((0, 7)\): \( (2\times0, 2\times7)=(0, 14) \)
• For \((4, 4)\): \( (2\times4, 2\times4)=(8, 8) \)
• For \((4, 1)\): \( (2\times4, 2\times1)=(8, 2) \)
• For \((2, 1)\): \( (2\times2, 2\times1)=(4, 2) \)

Step3: Plot the new vertices

Use the Polygon tool to plot the points \((0, 14)\), \((8, 8)\), \((8, 2)\), \((4, 2)\) and connect them to form the dilated figure.

Answer:

The dilated figure has vertices at \((0, 14)\), \((8, 8)\), \((8, 2)\), \((4, 2)\) (plotted using the Polygon tool as per the steps).