Reflections review

A reflection is a type of transformation that takes each point in a figure and reflects it over a line.

This reflection maps $\triangle{ABC}$triangle, A, B, C onto the blue triangle over the gold line of reflection.

The result is a new figure, called the image. The image is congruent to the original figure.

The line of reflection is usually given in the form $y = mx + b$y, equals, m, x, plus, b.

Each point in the starting figure is the same perpendicular distance from the line of reflection as its corresponding point in the image.

Reflect $\overline{PQ}$start overline, P, Q, end overline over the line $y=x$y, equals, x.

First, we must find the line of reflection $y=x$y, equals, x. The slope is $1$1 and the $y$y intercept is $0$0.

When the points that make up $\overline{PQ}$start overline, P, Q, end overline are reflected over the line $y=x$y, equals, x, they travel in a direction perpendicular to the line and appear the same distance from the line on the other side.

Note that in the case of reflection over the line $y=x$y, equals, x, every point $(a,b)$left parenthesis, a, comma, b, right parenthesis is reflected onto an image point $(b,a)$left parenthesis, b, comma, a, right parenthesis.

Reflecting over the line $y=x$y, equals, x maps $\overline{PQ}$start overline, P, Q, end overline onto the blue line below.

Want to try more problems like this? Check out this exercise.