JEE Main · 2021 · 26 Feb 2021 · Shift 1 · Straight Lines

The intersection of three lines

x - y = 0, x + 2 y = 3

and

2 x + y = 6

is a :

(A)Right angled triangle
(B)Isosceles triangle✓ Correct
(C)Equilateral triangle
(D)None of the above

Answer: (B)

Solution

Find the three vertices by solving pairs of equations.

x - y = 0

and

x + 2 y = 3

gives

x = y

and

3 y = 3

, so

(1, 1)

x - y = 0

and

2 x + y = 6

gives

x = y

and

3 x = 6

, so

(2, 2)

x + 2 y = 3

and

2 x + y = 6

gives

x = 3 - 2 y

and

2 (3 - 2 y) + y = 6

, so

6 - 3 y = 6

y = 0

x = 3

, giving

(3, 0)

. Calculate distances:

d_{12} = (2 - 1)^{2} + (2 - 1)^{2} = 2

d_{13} = (3 - 1)^{2} + (0 - 1)^{2} = 5

d_{23} = (3 - 2)^{2} + (0 - 2)^{2} = 5

. Since two sides are equal, it is an isosceles triangle.

JEE Main · 2021 · 26 Feb 2021 · Shift 1 · Single correct option

Practise more: all JEE Main PYQs on Straight Lines →

More JEE Main questions on Straight Lines

Let a point A lie between the parallel lines $L_{1}$ and $L_{2}$ such that its distances from $L_{1}$ and $L_{2}$ are 6 and 3 units, respectively. Then the area (in sq. units) of the equilateral triangle ABC , where the points B and C l …
JEE Main 2026View solution →
Among the statements
(S1): If $A (5, - 1)$ and $B (- 2, 3)$ are two vertices of a triangle, whose orthocentre is $(0, 0)$ , then its third vertex is $(- 4, - 7)$ and
(S2): If positive numbers $2 a, b, c$ are three consecutive terms of an A.P., then the lines $a x + b y + c = 0$ are …
JEE Main 2026View solution →
A rectangle is formed by the lines $x = 0$ , $y = 0$ , $x = 3$ and $y = 4$ . Let the line L be perpendicular to $3 x + y + 6 = 0$ and divide the area of the rectangle into two equal parts. Then the distance of the point $(\frac{1}{2}, - 5)$ …
JEE Main 2026View solution →
Let $A (1, 2)$ and $C (- 3, - 6)$ be two diagonally opposite vertices of a rhombus, whose sides AD and BC are parallel to the line $7 x - y = 14$ . If $B (α, β)$ and $D (γ, δ)$ are the other two vertices, then …
JEE Main 2026View solution →
Let $A (1, 0), B (2, - 1)$ and $C (\frac{7}{3}, \frac{4}{3})$ be three points. If the equation of the bisector of the angle ABC is $α x + β y = 5$ , then the value of $α^{2} + β^{2}$ is
JEE Main 2026View solution →
Let the angles made with the positive x-axis by two straight lines drawn from the point $P (2, 3)$ and meeting the line $x + y = 6$ at a distance $\frac{2}{3}$ from the point P be $θ_{1}$ and $θ_{2}$ . Then the value of …
JEE Main 2026View solution →