Question

lesson practice 2.1.03
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.

problems 4 - 5: imagine there is a quadrilateral b that is a scaled copy of quadrilateral a. its shortest side is 3 units long.
what is the scale factor from quadrilateral a to b?
draw quadrilateral b.

Explanation:

Step1: For problem 1

To draw a scaled - copy with a scale factor of 2, multiply the coordinates of each vertex of the polygon by 2. If a vertex of the original polygon has coordinates \((x,y)\), the corresponding vertex of the scaled - copy has coordinates \((2x,2y)\).

Step2: For problem 2

Let the side - lengths of the original polygon be \(a_1,a_2,\cdots,a_n\). The perimeter \(P\) of the original polygon is \(P=\sum_{i = 1}^{n}a_i\). The side - lengths of the scaled polygon with scale factor \(k = 2\) are \(b_i=k\times a_i = 2a_i\). So the perimeter of the scaled polygon \(P_{scaled}=k\times P=2P\).
If the area of the original polygon is \(A\), the area of the scaled polygon \(A_{scaled}=k^{2}A = 4A\). First, find the area and perimeter of the original polygon (by counting unit squares for area and adding side - lengths for perimeter), then use the scale - factor relationships.

Step3: For problem 3

To draw a scaled copy of figure \(ABCD\) with a scale factor of \(1.5\), if a vertex of figure \(ABCD\) has coordinates \((x,y)\), the corresponding vertex of the scaled figure has coordinates \((1.5x,1.5y)\).

Step4: For problem 4

Let the length of the shortest side of quadrilateral \(A\) be \(s_A\) and the length of the shortest side of quadrilateral \(B\) be \(s_B\). The scale factor \(k\) from quadrilateral \(A\) to quadrilateral \(B\) is given by \(k=\frac{s_B}{s_A}\).

Step5: For problem 5

Use the scale factor found in problem 4. Multiply the coordinates of each vertex of quadrilateral \(A\) by the scale factor to get the coordinates of the vertices of quadrilateral \(B\) and then draw it.

Since we don't have the actual side - lengths and coordinates of the polygons and quadrilaterals from the image (only the instructions), we can't give numerical answers. But the general methods are as above.

Answer:

1. Follow the rule of multiplying vertex coordinates by 2 to draw the scaled polygon.
2. Use \(P_{scaled}=2P\) and \(A_{scaled}=4A\) after finding \(P\) and \(A\) of the original polygon.
3. Multiply vertex coordinates of \(ABCD\) by 1.5 to draw the scaled figure.
4. Calculate \(k = \frac{s_B}{s_A}\) for the scale factor from \(A\) to \(B\).
5. Use the scale factor from 4 to find vertex coordinates of \(B\) and draw it.