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how to prove prove that the feet of the perpendiculars from the origin on the lines x+y=4, x+5y= 26 and 15x -27y = 424 are collinear

how to prove prove that the feet of the perpendiculars from the origin on the lines x+y=4, x+5y= 26 and 15x -27y = 424 are collinear

Grade:11

1 Answers

Vikas TU
14149 Points
4 years ago
Find its eqn. simply and U will let it know.
simple as that.
For that U need a point and slope.
point is given (0,0)
and slope is also given.
 
For x+y=4
m1 = 1
thus y = x
 
For x+5y= 26
m2 = 5
y = 5x
 
For  15x -27y = 424
m3 = -27/15 or -9/5
y = (-9/5)x
 
Now solve each determined eqns. with
the three given eqns.
and get the foot.
To check collinearity,
calculate the slope using any two feet
and compare.
it will be same.

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