Question

Enter the rule used to transform triangle ABC . If there is a dilation, dilate with respect to the origin. The rule used to transform triangle ABC(x,y)

Answer 1

There is a dilation and the scale factor is 4

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:

`k = (Original)/(Image)`

Using A and A'

`k = (A)/(A')`

`k = ((2,5))/((0.5,1.25))`

Factorize the numerator

`k = (4(0.5,1.25))/((0.5,1.25))`

`k = 4*((0.5,1.25))/((0.5,1.25))`

`k = 4 * 1`

`k =4`

Using B and B'

`k = (B)/(B')`

`k = ((6,10))/((1.5, 2.5))`

Factorize the numerator

`k = (4(1.5, 2.5))/((1.5, 2.5))`

`k = 4*((1.5, 2.5))/((1.5, 2.5))`

`k = 4 * 1`

`k =4`

Using C and C'

`k = (C)/(C')`

`k = ((9, -1))/((2.25, -0.25))`

Factorize the numerator

`k = (4(2.25, -0.25))/((2.25, -0.25))`

`k = 4*((2.25, -0.25))/((2.25, -0.25))`

`k = 4*((2.25, -0.25))/((2.25, -0.25))`

`k = 4 * 1`

`k =4`

The above shows that k is 4 in all cases.

Hence, there is a dilation and the scale factor is 4