The scale factor of dilation from ABC to A’B’C’ is 2.5.
Step-by-step explanation:
Step 1:
First, we plot the coordinates of both triangles.
The coordinates of triangle ABC are as follows;
A = (0, 2), B = (2, 2), and C = (2,0).
The coordinates of triangle A’B’C’ are;
A’= (-4, -1), B’= (1, -1), and C’ = (1, -6).
Step 2:
Next, we need to find the distances between at least to coordinates for both triangles.
The distances between vertical lines are found by calculating the difference in y values while for horizontal lines, the distances are found by calculating the difference between the x values.
The distance of AB = 2 - 0 = 2 units, the distance of BC = 2 - 0 = 2 units.
The distance of A’B’ = 1 - (-4) = 5 units, the distance of B’C’ = 6 - 1 = 5 units (both points are negative y)
Step 3:
To calculate the scale factor, we divide the measurement after scaling by the same measurement before scaling.
In this case, it is the length of the AB. So the scale factor = [tex]\frac{5}{2}[/tex] = 2.5.
The scale factor for line BC = [tex]\frac{5}{2}[/tex] = 2.5.
