Question

The endpoints of are A(2, 2) and B(3, 8). is dilated by a scale factor of 3.5 with the origin as the center of dilation to give image . What are the slope (m) and length of ? Use the distance formula to help you decide: .

Answer 1

The slope is m=6 and length of line is
`d' =3.5√(37)`

Explanation:

Given : The endpoints of line AB are A(2, 2) and B(3, 8). Line AB is dilated by a scale factor of 3.5 with the origin as the center of dilation to give image line A'B' .

To find : What are the slope (m) and length of line AB?

Solution :

The slope of a line does not change.

Slope formula is,

`m=(y_2-y_1)/(x_2-x_1)`

The slope of AB A(2, 2) and B(3, 8) is :

`m=(8-2)/(3-2)\\\\m=(6)/(1)\\\\m=6`

Distance formula,
`d = √((x_2-x_1)^2 + (y_2-y_1)^2)`

The length of AB by distance formula,

`d = √((3 - 2)^2+(8-2)^2)\\d = √((1)^2+(6)^2)\\d=√(1+36)\\d=√(37)`

Line AB is dilated by a scale factor of 3.5.

The length of A'B' is :

`d' =3.5*√(37)\\d' =3.5√(37)`

Therefore, The slope is m=6 and length of line is
`d' =3.5√(37)`

Answer 2

m=6,a'b'=3.5 square root 37