Visual SolutionPYQ 2024 · Jan Shift 2Standard

Question

Let A be the point of intersection of the lines

3x + 2y = 14

5x - y = 6

and B be the point of intersection of the lines

4x + 3y = 8

6x + y = 5

. The distance of the point

P(5, -2)

from the line AB is:

(A)

\frac{13}{2}

(B)

8

(C)

\frac{5}{2}

(D)

6

Solution Path

Find

A(2,4)

and

B(\tfrac{1}{2},2)

. Line AB:

4x-3y+4=0

. Distance from

P(5,-2) = \frac{30}{5} = 6

01Question Setup

1/4

Find the distance of

P(5, -2)

from line

AB

, where

A

and

B

are intersections of given line pairs.

d = \;?

02Find A and B

2/4

Solve each pair:

A = (2, 4)

from

3x+2y=14,\; 5x-y=6

B = (\frac{1}{2}, 2)

from

4x+3y=8,\; 6x+y=5

A(2,4),\; B(\tfrac{1}{2}, 2)

03Line AB and DistanceKEY INSIGHT

3/4

Slope

= \frac{4}{3}

, so line AB:

4x - 3y + 4 = 0

. Distance

= \frac{|20+6+4|}{5} = 6

d = 6

04Final Answer

4/4

Distance of

P(5,-2)

from line

AB

6

\boxed{6}

Concepts from this question1 concepts unlocked

★

EASY

Distance from (x₁, y₁) to line ax + by + c = 0 is |ax₁ + by₁ + c| / √(a² + b²).

d = \frac{|ax_1 + by_1 + c|}{\sqrt{a^2 + b^2}}

Used in area calculations, mirror image, and foot of perpendicular problems. High-frequency JEE formula.

Distance problemsArea of triangleFoot of perpendicular

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