Question

Dilate line f by a scale factor of 2 with the center of dilation at the origin to create line f. Where are points A' and B' located after dilation, and how are lines fand f related?

(A) The locations of A' and B' are A' (0,4) and B' (4,0); lines f and f are parallel.

(B) The locations of A' and B' are A' (0, 2) and B' (2, 0); lines f and f are the same line.

(c) The locations of A' and B' are A' (0, 2) and B' (4, ); lines f and f intersect at point A.

(D) The locations of A' and B' are A' (0,4) and B' (2, 0); lines f and f intersect at point B.​

Answer 1

Option A

Explanation:

We are given that

Scale factor=2

Center of dilation=(0,0)

Point A(0,2) and point B (2,0).

Slope of line f=
`(y_2-y_1)/(x_2-x_1)`

Substitute the values

Slope of line f=
`(0-2)/(2-0)=-1`

Distance between A and Origin (0,0) is given by

`OA=√((0-0)^2+(0-2)^2)=2 units`

Using distance formula

`√((x_2-x_1)^2+(y_2-y_1)^2)`

OB=
`√((0-2)^2+(0-0)^2)=2 units`

Length of OA'=2OA=2(2)=4 units

Length of OB'=2(OB)=2(2)=4 units

x-intercept of line f' at x=4

y-intercept of line f' at y=4

Therefore, the points A' and B' are given by

(0,4) and (4,0)

Slope of line f'=
`(0-4)/(4-0)=-1`

Slope of line f and f' are equal.Therefore, lines f and f' are parallel.

Option A is true.