Question

The scale factor K is PLEASE ANSWER AND EXPLAIN PEASEE

Answer 1

Scale factor K equals 4.

Step-by-step explanation:

Step 1; First we plot points $A^{1}$, $B^{1}$, $C^{1}$ and $D^{1}$ on the graph. Coordinates are  (4, 8), $B^{1}$ (12, 16), $C^{1}$ (20, 8), and $D^{1}$(20, 0). We need to find the distance between at least 2 sides of the polygon i.e $A^{1}$$B^{1}$ and

Step 2; To find the distances of $A^{1}$$B^{1}$ and

Distance = √ (x2 - x1)² + (y2 - y1)².

Distance between $A^{1}$(4, 8) and $B^{1}$ (12, 16) where $A^{1}$ is (x1, y1) and $B^{1}$ is      (x2, y2).

Distance = √ (12 - 4)² + (16 - 8)² = √ 64 + 64 = √128 = 11.313 units

Similarly distance between $B^{1}$ (12, 16) and $C^{1}$ (20, 8), where $B^{1}$ is (x1, y1) and $C^{1}$ is (x2, y2).

Distance = √ (20 - 12)² + (8 - 16)² = √ 64 + 64 = √128 = 11.313 units

Step 3; Now we need to do the same for points A(4, 4), B(6, 6), C(8, 4), and D(8, 2).

Distance between A(4, 4) and B(6, 6) where A is (x1, y1) and B is (x2, y2).

Distance = √ (6 - 4)² + (6 - 4)² = √ 4 + 4 = √8 = 2.828 units

Similarly distance between B(6, 6) and C(8, 4) , where B is (x1, y1) and C is  (x2, y2).

Distance = √ (8 - 6)² + (4 - 6)² = √ 4 + 4 = √8 = 2.828 units.

Step 4; To calculate the scale factor, we divide the scaled distance by the original distance. So

Scale factor = $\frac{11.313}{2.828}$ = 4.2223 which is approximately equal to 4.