Answer:
There is a dilation and the scale factor is 4
Step-by-step explanation:
The details that complete the question are:
△ABC
A(2, 5), B(6, 10), C(9, −1)
△A′B′C′
A′(0.5, 1.25), B′(1.5, 2.5), C′(2.25, −0.25)
Checking if there is dilation or not
To do this, we make use of the following scale factor (k) formula:
[tex]k = \frac{Original}{Image}[/tex]
Using A and A'
[tex]k = \frac{A}{A'}[/tex]
[tex]k = \frac{(2,5)}{(0.5,1.25)}[/tex]
Factorize the numerator
[tex]k = \frac{4(0.5,1.25)}{(0.5,1.25)}[/tex]
[tex]k = 4*\frac{(0.5,1.25)}{(0.5,1.25)}[/tex]
[tex]k = 4 * 1[/tex]
[tex]k =4[/tex]
Using B and B'
[tex]k = \frac{B}{B'}[/tex]
[tex]k = \frac{(6,10)}{(1.5, 2.5)}[/tex]
Factorize the numerator
[tex]k = \frac{4(1.5, 2.5)}{(1.5, 2.5)}[/tex]
[tex]k = 4*\frac{(1.5, 2.5)}{(1.5, 2.5)}[/tex]
[tex]k = 4 * 1[/tex]
[tex]k =4[/tex]
Using C and C'
[tex]k = \frac{C}{C'}[/tex]
[tex]k = \frac{(9, -1)}{(2.25, -0.25)}[/tex]
Factorize the numerator
[tex]k = \frac{4(2.25, -0.25)}{(2.25, -0.25)}[/tex]
[tex]k = 4*\frac{(2.25, -0.25)}{(2.25, -0.25)}[/tex]
[tex]k = 4*\frac{(2.25, -0.25)}{(2.25, -0.25)}[/tex]
[tex]k = 4 * 1[/tex]
[tex]k =4[/tex]
The above shows that k is 4 in all cases.
Hence, there is a dilation and the scale factor is 4
