Find the mirror image of this line I have a homework assignment that I just can't solve.
The point (3.4) is reflected on the line $y = 2x +1$. Which coordinates are the mirror image.
I know that I have to use the following formula $y = kx+m$ but do not know how.
Thanks!!
 A: Actually, you have to draw a perpendicular line to the original line which includes $P(3,4)$. The condition for perpendicular lines is $k_1\cdot k_2=-1$. Therefore, perpendicular line should be:
$$y=\frac{-1}{2}x+m$$
You can find $m=\frac{11}{2}$ by putting $P(3,4)$.
Now you have to find the intersection point $P(x_c,y_c)$ by calculating:
$$2x_c+1=\frac{-1}{2}x_c+\frac{11}{2}$$
Then $P(x_c,y_c)$ will be the center of your mirror. You can find the reflection with the middle point formulas:
$$x_c=\frac{x_2+x_1}{2} \;\;\;\; y_c=\frac{y_2+y_1}{2}$$
A: There are 3 paralel lines here. Sketch or plot line parallel to given line through given point. i.e.,solve for unknown c in y = 2 x + c. Observe y-intercepts and see how the intercept of given line can be made exactly in between c of this line and c of the required line.
By this procedure, y = 2 x - 2 contains given point (3,4), y = 2 x + 4 is the required line mirrored by given line y = 2 x + 1. Their y- intercepts (-2,1,4) are in arithmetic progression.
