A line passing through the origin perpendicularly cuts the line 3x - 2y = 6 at point M. Find M?

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14 vote

A line passing through the origin perpendicularly cuts the line 3x - 2y = 6 at point M. Find M?

Asked on 2019-07-19 22:09:07 by Guest | Votes 14 | Views: 406 | Tags: geometry | quantitative aptitude | Add Bounty

A line passing through the origin perpendicularly cuts the line 3x - 2y = 6 at point M. Find M?

1). (18/13, 12/13)
2). (18/13, -12/13)
3). (-18/13, -12/13)
4). (-18/13, 12/13)

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1 answers

18 vote

Answered by Guest on 2019-07-19 22:12:02 | Votes 18 | #

Equation of a line passing through the origin is y = ax, where a is slope.

Given, line passing through the origin perpendicularly cuts the line 3x - 2y = 6.

Two lines are perpendicular to each other when product of their slopes is - 1.

∴ a × 3/2 = - 1

⇒ a = -2/3

Equation of lines is y = -2x/3

They meet at point M.

3x + 4x/3 = 6

⇒ x = 18/13

54/13 - 2y = 6

⇒ y = - 12/13

∴ M is (18/13, -12/13)

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