Question

The perpendicular from the origin intersects the line √32x+12y=532x+12y=5 at the coordinates:

(52,5√3252,532)

(5√32,52532,52)

(−5√32,52−532,52)

(5√32,−52532,−52)​

Answer 1

Given :   (√3 / 2) x + (1/2)y = 5

To Find : perpendicular from the origin intersects the line at the coordinates​

Solution:

(√3 / 2) x + (1/2)y = 5

=> (√3) x + y = 10

=> y = -√3  x  + 10

=> Slope = - √3

Hence Slope of perpendicular must be:   1/√3

Perpendicular from origin

Hence y =  x/√3

(√3 / 2) x + (1/2)y = 5

=>  (√3 / 2) x + (1/2) x/√3 = 5

=> 3x + x = 10√3

=> x = 5√3/2

  y = 5/2

The perpendicular from the origin intersects the line√3/2x+1/2y=5

at the coordinates​ ( 5√3/2 ,  5/2)

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