Question

Which transformation of AB will produce a line segment A'B' that is parallel to AB?

Answer 1

Options:

Rotation of 180° about point B

Rotation of 90° about point b

Reflection over the x-axis

Translation down 2 units

Answer:

Rotation of 180° about point B

Explanation:

Considering coordinates of point B

Assume the coordinates of the line at point B is (x,y)

i.e.
`B = (x,y)`

First, we need to determine the slope at point B

Taking coordinates about the origin.

The slope of B is:

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

Where

`(x_1,y_1) = (0,0)` --- origin

`(x_2,y_2) = (x,y)`

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

`m = (y - 0)/(x - 0)`

`m = (y)/(x)`

Taking the options one after the other:

Option A.

When rotated by 180°, the resulting coordinates of B would be

`B' = (-x,-y)`

Taking the slope of B'

The slope of B is:

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

Where

`(x_1,y_1) = (0,0)` --- origin

`(x_2,y_2) = (-x,-y)`

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

`m = (-y - 0)/(-x - 0)`

`m = (-y)/(-x)`

`m = (y)/(x)`

Notice that the slope of B and B' is the same;

`m = (y)/(x)`

Hence:

Rotation of 180° about point B answers the question

There's no need to check for other options