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
Step-by-step explanation:
Considering coordinates of point B
Assume the coordinates of the line at point B is (x,y)
i.e. [tex]B = (x,y)[/tex]
First, we need to determine the slope at point B
Taking coordinates about the origin.
The slope of B is:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Where
[tex](x_1,y_1) = (0,0)[/tex] --- origin
[tex](x_2,y_2) = (x,y)[/tex]
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex] becomes
[tex]m = \frac{y - 0}{x - 0}[/tex]
[tex]m = \frac{y}{x}[/tex]
Taking the options one after the other:
Option A.
When rotated by 180°, the resulting coordinates of B would be
[tex]B' = (-x,-y)[/tex]
Taking the slope of B'
The slope of B is:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Where
[tex](x_1,y_1) = (0,0)[/tex] --- origin
[tex](x_2,y_2) = (-x,-y)[/tex]
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex] becomes
[tex]m = \frac{-y - 0}{-x - 0}[/tex]
[tex]m = \frac{-y}{-x}[/tex]
[tex]m = \frac{y}{x}[/tex]
Notice that the slope of B and B' is the same;
[tex]m = \frac{y}{x}[/tex]
Hence:
Rotation of 180° about point B answers the question
There's no need to check for other options
