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