# Reflections on a Coordinate Plane

This video is an extension of video mathematics -Transformations: Reflections.

To get a general explanation please watch other videos.

Problem: Reflect the triangle with the vertices of (-1,-2), (-2,1) and (0,3) over the y=x line.

Step 1  Graph vertices and mirror line

 Step 2  Find equations of lines perpendicular to mirror the line that passes through each vertex using the point-slope equation. mirror line y=x Slope=1 perpendicular lines slope is negative reciprocal. Slope = -1
Point A (-1,-2) Point B (-2,1) Point C (0,3)
y+2=-1(x+1) y-1=-1(x+2) y-3=-1(x-0)
y+2=-x-1 y-1=-x-2 y-3=-x
y=-x-3 y=-x-1 y=-x+3

Step 3 Solve system of mirror line and perpendicular line to find intersection point on the mirror line.
In all intersections y=x, substitute y=x

Line A y=-x-3 Line B y=-x-1 Line C y=-x+3
x=-x-3 x=-x-1 x=-x+3
2x=-3 2x-1 2x=3
x=-1.5 x=-0.5 x=1.5
y=-1.5 y=-0.5 y=-1.5

Step 4Determine distance between point on mirror line and vertex.
* From now on I’m only going to show calculations for point A. In order to find other mirror vertices, repeat calculations for B and C

Point A (-1,-2),(-1.5,-1.5)

Step 5 Find point opposite of the initial vertex that lies on the perpendiclarline that has the same distance from the mirror line as to the original vertex.
Point A

substitute y=-x-3