Q. 165.0( 1 Vote )

# Find the coordina

Here we have a perpendicular from the origin i.e.(0,0) to the

straight line 3x + 2y = 13.

We have to find the foot of the perpendicular i.e the intersection point at the line 3x + 2y = 13.

As these lines are perpendicular the product of their slopes is equal to –1.

Slope of the 3x + 2y–13 = 0 is m. Therefore the slope of perpendicular is i.e. Hence the equation of the perpendicular from (0,0) and slope as is (y–y1) = m(x–x1)  3y = 2x

3y–2x = 0

2x–3y = 0

Now solve the two equations 3x + 2y–13 = 0 and 2x–3y = 0.

3x + 2y–13 = 0–––(1)

2x–3y = 0–––––(2)

Multiply (1) by 3 and (2) by 2 and add  Substitute x = 3 in the equation 2x–3y = 0.

2(3)–3y = 0

–3y = –6

y = 2(Divide both the sides of the equation by –3)

Hence the coordinates of the foot of the perpendicular is(3,2)

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