SOLUTION: The diagonals of rhombus LMAO intersect at P(4,11). If the equation of the line that contains diagonal LA is Y=2X +3, what is the equation of a line that contains diagonal MO

Question 1180683: The diagonals of rhombus LMAO intersect at P(4,11). If the equation of the line that contains diagonal LA is Y=2X +3, what is the equation of a line that contains diagonal MO
Answer by amarjeeth123(570) (Show Source): You can put this solution on YOUR website!
The diagonals of rhombus LMAO intersect at P(4,11).
If the equation of the line that contains diagonal LA is Y=2X +3
In a rhombus,the diagonals are perpendicular to each other.
The equation of the first diagonal LA is Y=2X+3
Comparing this with the equation y=mx+c we get,
Slope of the first diagonal m1=2
y-intercept c1=3
Since the diagonals are perpendicular, slope of the second diagonal m2=(-1/2).
Let the equation of the second diagonal be y=(-1/2)x+c2 where c2 is a constant.
Since it passes through the point P(4,11) we have
11=-2+c2
c2=13
The equation of the line that contains the other diagonal MO is y=(-1/2)x+13
Multiplying by 2 on both sides we get,
2y=-x+26
x+2y=26
x+2y-26=0
Answer is x+2y-26=0
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