A line segment has endpoints at (5 ,8 ) and (7 ,4). If the line segment is rotated about the origin by pi , translated horizontally by -1 , and reflected about the y-axis, what will the line segment's new endpoints be?

1 Answer
Jan 21, 2016

(6,-8),(8,-4)

Explanation:

We can create a rule for this transformation.

Assume the original endpoints of the segment can be described as color(red)((x,y).

The first way in which the segment is manipulated is with a rotation of pi, or 180^@. This translates by taking the opposite of the x and y values of the point, or our new "rule" for this point in the transformation: color(red)((-x,-y)

The endpoints are then translated horizontally by -1. Horizontal movement corresponds to the x coordinate, whereas vertical corresponds to the y coordinate. Since this has been horizontally shifted, the new rule, working off the most previous rule, is: color(red)((-x-1,-y)

The final transformation is a reflection over the y axis, which means that the x coordinate's sign is flipped: color(red)((x+1,-y)

This is the rule for the entire transformation. Apply it to the points (5,8) and (7,4).

(5,8)rarr(6,-8)

(7,4)rarr(8,-4)