Question

If the image of (-7/5,-6/5) in a line is (1,2) then the equation of the line is

Answer 1

Given:  Image of (-7/5,-6/5) in a line is (1,2).

To find: The equation of the line?

Solution:

Consider a line: y = mx + c.

We have a point  (-7/5,-6/5) above a line and its mirror image is at (1,2), so line will be mx - y + c = 0

Now if we have a point x1,y1 and equation is ax+by+c=0 then the mirror image is found out by:

            x-x1/a = y-y1/b = -2(ax1+by1+c) / a^2 + b^2

So putting values in formula we get:

            1 - (-7/5) / m = 2 - (-6/5) / -1 = -2(-7/5m - (-6/5) + c ) / m^2+1

            12/5m = -16/5 = -2(-7/5m+6/5+c) /  m^2+1

So equating 12/5m = -16/5, we get:

            m = -3/4

Now equating -16/5 = -2(-7/5m+6/5+c) /  m^2+1, we get:

           -16/5 = -2(-28/15+6/5+c) /  9/16 +1

           -16/5 = (56/15-12/5-2c) /  9/16 +1

           -16/5 x 25/16 = 20/15 - 2c

           -5 = 4/3 - 2c

           2c = 19/3

           c = 19/6

Answer:

               So the equation of line is: y = -3/4x + 19/6

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