If the line x - 4y - 6 = 0 is the perpendicular bisector of the line segment PQ and the coordinates of P are (1, 3), find the coordinates of Q.
Straight Line Eq
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Question

If the line x - 4y - 6 = 0 is the perpendicular bisector of the line segment PQ and the coordinates of P are (1, 3), find the coordinates of Q.

KnowledgeBoat · Accepted Answer

Given, equation of line, ⇒ x - 4y - 6 = 0 ⇒ 4y = x - 6 ⇒ y = Comparing with y = mx + c we get, slope = . Since, given line and PQ are perpendicular so their products will be equal to -1. Let slope of PQ be m₁, Hence, slope of PQ = -4. Now equation of PQ can be found by point slope form i.e., Since, line x - 4y - 6 = 0 is perpendicular bisector of 4x + y - 7 = 0 hence solving them simultaneously to find point of intersection, ⇒ x - 4y = 6 ......(i) ⇒ 4x + y = 7 ......(ii) Multiplying (ii) with 4 and adding with (i) we get, ⇒ 16x + 4y + x - 4y = 28 + 6 ⇒ 17x = 34 ⇒ x = 2. Putting value of x = 2 in (i), ⇒ 2 - 4y = 6 ⇒ -4y = 4 ⇒ y = -1. Hence, the point of intersection which is the mid-point of PQ is (2, -1). Let coordinates of Q be (a, b). By mid-point formula, coordinates of mid-point of PQ are Equating with mid-point of PQ (2, -1) we get, Hence, the coordinates of Q are (3, -5).

Mathematics

If the line x - 4y - 6 = 0 is the perpendicular bisector of the line segment PQ and the coordinates of P are (1, 3), find the coordinates of Q.

Straight Line Eq

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Mathematics

If the line x - 4y - 6 = 0 is the perpendicular bisector of the line segment PQ and the coordinates of P are (1, 3), find the coordinates of Q.

Straight Line Eq

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