Question

(Please answer before 5:15 P.M tonight)

Answer 1

The scale factor of dilation from ABC to $A^{1} B^{1} C^{1}$ is 0.333.

Step-by-step explanation:

Step 1:

First, we plot the coordinates of both triangles.

The coordinates of the triangle $A^{1} B^{1} C^{1}$ are as follows;

$A^{1}$ = (2, 3), $B^{1}$ = (2, 1), and $C^{1}$ = (3, 1).

The coordinates of triangle ABC are;

A = (4, 9), B = (4, 3), and C = (7, 3).

Step 2;

Next, we need to find the distances between at least two 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 $A^{1} B^{1} = 3-1=2$, the distance of $B^{1} C^{1} = 3-2=1$.

The distance of AB $=9-3=6,$ the distance of BC $= 7-4=3.$

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 for AB = $\frac{2}{6} = \frac{1}{3} = 0.333.$

The scale factor for BC = $\frac{1}{3} = 0.333.$