Area of Triangle

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JEE Main 2007

Let $A (h, k), B (1, 1)$ and $C (2, 1)$ be the vertices of a right angled triangle with $A C$ as its hypotenuse. If the area of the triangle is 1 square unit, then the set of values which 'k' can take is given by

{- 1, 3}

(B)

{- 3, - 2}

(C)

{1, 3}

(D)

{0, 2}

JEE Advanced 2008

LEVELJEE Main

Consider three points $P = (- sin (β - α), - cos β)$ , $Q = (cos (β - α), sin β)$ and $R = (cos (β - α + θ), sin (β - θ))$ , where $0 < α, β, θ < \frac{π}{4}$ . Then,

(A)

(a)

P

lies on the line segment

R Q

(B)

(b)

Q

lies on the line segment

P R

(C)

(c)

R

lies on the line segment

QP

(D)

(d)

P, Q, R

are non-collinear

JEE Advanced 1999

LEVELJEE Main

If $x_{1}, x_{2}, x_{3}$ as well as $y_{1}, y_{2}, y_{3}$ are in G.P. with the same common ratio, then the points $(x_{1}, y_{1}), (x_{2}, y_{2})$ and $(x_{3}, y_{3})$

(A)

lie on a straight line

are vertices of a triangle

JEE Advanced 2005

LEVELJEE Main

The area of the triangle formed by the intersection of a line parallel to x-axis and passing through $P (h, k)$ with the lines $y = x$ and $x + y = 2$ is $4 h^{2}$ . Find the locus of the point $P$ .

JEE Advanced 1983

LEVELBoard

The coordinates of $A, B, C$ are $(6, 3)$ , $(- 3, 5)$ , $(4, - 2)$ respectively, and $P$ is any point $(x, y)$ . Show that the ratio of the area of the triangles $△ P B C$ and $△ A B C$ is $∣ \frac{x + y - 2}{7} ∣$ .

JEE Advanced 1978

LEVELJEE Main

The area of a triangle is 5. Two of its vertices are $A (2, 1)$ and $B (3, - 2)$ . The third vertex $C$ lies on $y = x + 3$ . Find $C$ .

JEE Main 2019 (9 January)

LEVELJEE Main

Let $S$ be the set of all triangles in the xy-plane, each having one vertex at the origin and the other two vertices lie on coordinate axes with integral coordinates. If each triangle in $S$ has area 50 sq. units, then the number of elements in the set $S$ is:

JEE Main 2020 (8 January Shift 1)

LEVELJEE Main

Let two points be $A (1, - 1)$ and $B (0, 2)$ . If a point $P (x^{'}, y^{'})$ be such that the area of $Δ P A B = 5$ sq. units and it lies on the line, $3 x + y - 4 λ = 0$ , then the value of $λ$ is :

JEE Main 2020 - 8 Jan (Morning)

LEVELJEE Main

Let two points be $A (1, - 1)$ and $B (0, 2)$ . If a point $P (x^{'}, y^{'})$ be such that the area of $Δ P A B = 5$ square units and it lies on the line, $3 x + y - 4 λ = 0$ , then a value of $λ$ is:

JEE Main 2021 (01 Sep Shift 2)

LEVELJEE Main

Let the points of intersections of the lines $x - y + 1 = 0$ , $x - 2 y + 3 = 0$ and $2 x - 5 y + 11 = 0$ are the mid points of the sides of a triangle $A B C$ . Then the area of the triangle $A B C$ is .

JEE Main 2021 (March)

LEVELJEE Main

Let A(-1,1), B(3, 4) and C(2,0) be given three points. A line $y = m x, m > 0$ , intersects lines AC and BC at point P and Q respectively. Let $A_{1}$ and $A_{2}$ be the areas of $△ A B C$ and $△ P QC$ respectively, such that $A_{1} = 3 A_{2}$ , then the value of m is equal to :

(A)

\frac{4}{15}

(B)

(C)

(D)

JEE Main 2022 (24 June Shift 2)

LEVELJEE Main

Let the area of the triangle with vertices $A (1, α)$ , $B (α, 0)$ and $C (0, α)$ be 4 sq. units. If the point $(α, - α)$ , $(- α, α)$ and $(α^{2}, β)$ are collinear, then $β$ is equal to

JEE Main 2022 (28 June Shift 2)

LEVELJEE Advanced

Let a triangle be bounded by the lines $L_{1} : 2 x + 5 y = 10$ ; $L_{2} : - 4 x + 3 y = 12$ and the line $L_{3}$ , which passes through the point $P (2, 3)$ , intersect $L_{1}$ at $A$ and $L_{2}$ at $B$ . If the point $P$ divides the line-segment $A B$ , internally in the ratio $1 : 3$ , then the area of the triangle is equal to

(A)

\frac{110}{13}

(B)

\frac{132}{13}

(C)

\frac{142}{13}

(D)

\frac{151}{13}

JEE Main 2024 (05 Apr Shift 2)

LEVELJEE Main

Let $A (- 1, 1)$ and $B (2, 3)$ be two points and $P$ be a variable point above the line $A B$ such that the area of $△ P A B$ is 10. If the locus of $P$ is $a x + b y = 15$ , then $5 a + 2 b$ is :

(A)

(B)

- \frac{6}{5}

(C)

(D)

- \frac{12}{5}

JEE Main 2025 (April)

LEVELJEE Main

Let $A (4, - 2), B (1, 1)$ and $C (9, - 3)$ be the vertices of a triangle $A B C$ . Then the maximum area of the parallelogram $A F D E$ , formed with vertices $D, E$ and $F$ on the sides $B C, C A$ and $A B$ of the triangle $A B C$ respectively, is ______ .

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Consider three points P=(−sin(β−α),−cosβ), Q=(cos(β−α),sinβ) and R=(cos(β−α+θ),sin(β−θ)), where 0<α,β,θ<4π​. Then,

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If x1​,x2​,x3​ as well as y1​,y2​,y3​ are in G.P. with the same common ratio, then the points (x1​,y1​),(x2​,y2​) and (x3​,y3​)

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The area of a triangle is 5. Two of its vertices are A(2,1) and B(3,−2). The third vertex C lies on y=x+3. Find C.

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Let two points be A(1,−1) and B(0,2). If a point P(x′,y′) be such that the area of ΔPAB=5 sq. units and it lies on the line, 3x+y−4λ=0, then the value of λ is :

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Let two points be A(1,−1) and B(0,2). If a point P(x′,y′) be such that the area of ΔPAB=5 square units and it lies on the line, 3x+y−4λ=0, then a value of λ is:

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Let the points of intersections of the lines x−y+1=0, x−2y+3=0 and 2x−5y+11=0 are the mid points of the sides of a triangle ABC. Then the area of the triangle ABC is .

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Let the area of the triangle with vertices A(1,α), B(α,0) and C(0,α) be 4 sq. units. If the point (α,−α), (−α,α) and (α2,β) are collinear, then β is equal to

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Let A(−1,1) and B(2,3) be two points and P be a variable point above the line AB such that the area of △PAB is 10. If the locus of P is ax+by=15, then 5a+2b is :

Consider three points $P = (- sin (β - α), - cos β)$ , $Q = (cos (β - α), sin β)$ and $R = (cos (β - α + θ), sin (β - θ))$ , where $0 < α, β, θ < \frac{π}{4}$ . Then,

If $x_{1}, x_{2}, x_{3}$ as well as $y_{1}, y_{2}, y_{3}$ are in G.P. with the same common ratio, then the points $(x_{1}, y_{1}), (x_{2}, y_{2})$ and $(x_{3}, y_{3})$

The area of a triangle is 5. Two of its vertices are $A (2, 1)$ and $B (3, - 2)$ . The third vertex $C$ lies on $y = x + 3$ . Find $C$ .

Let two points be $A (1, - 1)$ and $B (0, 2)$ . If a point $P (x^{'}, y^{'})$ be such that the area of $Δ P A B = 5$ sq. units and it lies on the line, $3 x + y - 4 λ = 0$ , then the value of $λ$ is :

Let two points be $A (1, - 1)$ and $B (0, 2)$ . If a point $P (x^{'}, y^{'})$ be such that the area of $Δ P A B = 5$ square units and it lies on the line, $3 x + y - 4 λ = 0$ , then a value of $λ$ is:

Let the points of intersections of the lines $x - y + 1 = 0$ , $x - 2 y + 3 = 0$ and $2 x - 5 y + 11 = 0$ are the mid points of the sides of a triangle $A B C$ . Then the area of the triangle $A B C$ is .

Let the area of the triangle with vertices $A (1, α)$ , $B (α, 0)$ and $C (0, α)$ be 4 sq. units. If the point $(α, - α)$ , $(- α, α)$ and $(α^{2}, β)$ are collinear, then $β$ is equal to

Let $A (- 1, 1)$ and $B (2, 3)$ be two points and $P$ be a variable point above the line $A B$ such that the area of $△ P A B$ is 10. If the locus of $P$ is $a x + b y = 15$ , then $5 a + 2 b$ is :