Scale factor K equals 4.
Step-by-step explanation:
Step 1; First we plot points [tex]A^{1}[/tex], [tex]B^{1}[/tex], [tex]C^{1}[/tex] and [tex]D^{1}[/tex] on the graph. Coordinates are (4, 8), [tex]B^{1}[/tex] (12, 16), [tex]C^{1}[/tex] (20, 8), and [tex]D^{1}[/tex](20, 0). We need to find the distance between at least 2 sides of the polygon i.e [tex]A^{1}[/tex][tex]B^{1}[/tex] and
Step 2; To find the distances of [tex]A^{1}[/tex][tex]B^{1}[/tex] and
Distance = √ (x2 - x1)² + (y2 - y1)².
Distance between [tex]A^{1}[/tex](4, 8) and [tex]B^{1}[/tex] (12, 16) where [tex]A^{1}[/tex] is (x1, y1) and [tex]B^{1}[/tex] is (x2, y2).
Distance = √ (12 - 4)² + (16 - 8)² = √ 64 + 64 = √128 = 11.313 units
Similarly distance between [tex]B^{1}[/tex] (12, 16) and [tex]C^{1}[/tex] (20, 8), where [tex]B^{1}[/tex] is (x1, y1) and [tex]C^{1}[/tex] 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 = [tex]\frac{11.313}{2.828}[/tex] = 4.2223 which is approximately equal to 4.
