1. Line segment has endpoints of A(1,4) and B(-2,1), It is dilated and A’(3,12) and B(-6,3). What is the scale factor?
2. Triangle ABC has vertices A(0,3), B(3,6), and C(12,18). It is dilated with a scale factor of ⅓. Give the new vertices A’, B’, C’ using ordered pairs
3. If you would like to dilate a square with a side length of 8 units to create a square with a side length of 10 units, what scale factor should you use? Write your answer in decimal form.
4. Used a Scale factor of ⅔ to dilate a circle with radius of 18cm. What is radius or original circle?
5. A rectangle with w=2 and l=4 is similar to rectangle with length of 1. What is width of similar rectangle? (simplified fraction)
1. To find the scale factor, we can find the ratio of the change in corresponding x-coordinates to the change in corresponding y-coordinates.
The change in x for the original line segment is -2 - 1 = -3, and the change in x for the dilated line segment is -6 - 3 = -9.
The change in y for the original line segment is 1 - 4 = -3, and the change in y for the dilated line segment is 12 - 4 = 8.
The scale factor is therefore -9/-3 = 3.
2. To find the new vertices, we can multiply the x and y coordinates of each original vertex by the scale factor.
For vertex A, the new x-coordinate is 0 * 1/3 = 0 and the new y-coordinate is 3 * 1/3 = 1.
For vertex B, the new x-coordinate is 3 * 1/3 = 1 and the new y-coordinate is 6 * 1/3 = 2.
For vertex C, the new x-coordinate is 12 * 1/3 = 4 and the new y-coordinate is 18 * 1/3 = 6.
The new vertices are A'(0, 1), B'(1, 2), and C'(4, 6).
3. To find the scale factor, we can divide the new side length by the original side length.
The scale factor is 10/8 = 1.25.
4. To find the radius of the original circle, we can divide the radius of the dilated circle by the scale factor.
The radius of the original circle is (18 cm)/(2/3) = 27 cm.
5. The ratio of the widths of the two rectangles is equal to the scale factor.
Let the width of the similar rectangle be w'.
The scale factor is 2/1 = 2.
Therefore, w' = (2/1) * 2 = 4.
The width of the similar rectangle is 4.