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
perpendicular lines slope is negative reciprocal. Slope = -1
|Point A (-1,-2)||Point B (-2,1)||Point C (0,3)|
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|
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.
a=2, b=6, c=4
Original Vertex: x=-1 or Mirror Vertex: x=-2
mirror vertex of A=(-2,-1)