First slide

Equation of line in Straight lines

Question

Column - I Column - II
A ) If a, b, c are in A.P, then lines $a x + b y + c = 0$ are concurrent
B) A point on the line x + y = 4 which lies at a unit distance from the line 4x + 3y = 10 is
C) Orthocentre of triangle made by lines x + y = 1, x- y + 3 = 0, 2x + y = 7 is
D) Two vertices of a triangle are (5, -1) and (-2,3). If orthocentre is the origin then coordinate of the third vertex are
p) $(- 4, - 7)$
q) $(- 7, 11)$
r) $(1, - 2)$
s) $(- 1, 2)$
t) $(3, 1)$

Moderate

A

A-r, B-q,t, C-s,D-p
B

A-q,t, B-s, C-p, D-r
C

A-r, B-p, C-s, D-q,t
D

A-r,s B-s,p C-p, D-q,t

Solution

A) $a + c = 2 b \Rightarrow a + c - 2 b = 0$ $\Rightarrow a x + b y + c = 0$ Satisfies (1, -2)
B) Perpendicular distance of $P (λ, 4 - λ)$ from $4 x + 3 y = 10$
$\frac{| 4 λ + 3 (4 - λ) - 10 |}{5} = 1$
$\Rightarrow | λ + 2 | = 5 \Rightarrow λ - 2 \pm 5 = 3, - 7$
$P (3, 1), (- 7, + 11)$
C) Point $B = (- 1, 2)$
D) $\frac{y}{x} = \frac{7}{4}$
$\frac{4 + 1}{y - 5} = \frac{2}{3}, \frac{21}{4} x = 2 x - 13$
$x = - 4, y = - 7$

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