Question

problems 1 - 2: here is a polygon. 1. draw a scaled copy of the polygon using a scale factor of 2. 2. what is the area and perimeter of your scaled copy? 3. draw a scaled copy of figure abcd using a scale factor of 1.5.

Explanation:

Step1: Recall scaling - factor rules for perimeter and area

If the scale - factor of a scaled copy of a polygon is \(k\), the perimeter of the scaled copy is \(k\) times the perimeter of the original polygon, and the area of the scaled copy is \(k^{2}\) times the area of the original polygon.

Step2: For problem 1

To draw a scaled copy of the polygon with a scale - factor of 2, multiply the coordinates of each vertex of the original polygon by 2 if it is on a coordinate grid. If not on a grid, measure the lengths of the sides of the original polygon and multiply each side - length by 2 to construct the new polygon.

Step3: For problem 2

Let the perimeter of the original polygon be \(P\) and the area be \(A\). Since the scale - factor \(k = 2\), the perimeter of the scaled copy \(P_{new}=kP = 2P\), and the area of the scaled copy \(A_{new}=k^{2}A=4A\).

Step4: For problem 3

To draw a scaled copy of figure \(ABCD\) with a scale - factor of 1.5, if it is on a coordinate grid, multiply the coordinates of each vertex of figure \(ABCD\) by 1.5. If not on a grid, measure the lengths of the sides of figure \(ABCD\) and multiply each side - length by 1.5 to construct the new figure.

Answer:

1. Follow the side - length or coordinate - multiplication method to draw the scaled polygon with a scale - factor of 2.
2. The perimeter of the scaled copy is 2 times the perimeter of the original polygon, and the area of the scaled copy is 4 times the area of the original polygon.
3. Follow the side - length or coordinate - multiplication method to draw the scaled copy of figure \(ABCD\) with a scale - factor of 1.5.