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 f and f' related?
The locations of A' and B' are A' (0, 4) and B' (4, 0); lines f and f' are parallel.
The locations of A' and B' are A' (0, 2) and B' (2, 0); lines f and f' are the same line.
The locations of A' and B' are A' (0, 2) and B' (4, 0); lines f and f' intersect at point A.
The locations of A' and B' are A' (0, 4) and B' (2, 0); lines f and f' intersect at point B

Answer 1

Answer:

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

Step-by-step explanation:

Answer 2

Answer:

Option (1).

Step-by-step explanation:

Given question is incomplete: find the complete question in the attachment.

From the given figure, coordinates of the points A and B are (0, 2) and (2, 0) respectively.

Slope of line AB = $\frac{(y_{2}-y_{1})}{(x_{2}-x_{1})}$

                      $m_{1}=\frac{2-0}{0-2}=-1$

When these points are dilated by a scale factor = 2, about the origin

Rule for the dilation → (x, y) → (kx, ky)

Where k = scale factor

Coordinates of the points A' and B' will be (0, 4) and (4, 0)

Slope of the line A'B' = $\frac{(y_{2}-y_{1})}{(x_{2}-x_{1})}$

                             $m_{2}=\frac{4-0}{0-4}=-1$

Since $m_{1}=m_{2}$ , both the lines AB and A'B' will be parallel.

Therefore, option (1) will be the answer.