JEE Main 2022 · 27 Jul · Shift 1 · Mathematics Q18

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MathematicsSingle correct+4 / -1Question 18 of 90

Let A(1, 1), B(−4, 3), C(−2, −5) be vertices of a triangle ABC, P be a point on side BC, and $\Delta_1$ and $\Delta_2$ be the areas of triangles APB and ABC, respectively. If $\Delta_1:\Delta_2=4:7$ , then the area enclosed by the lines AP, AC and the $x$ -axis is

\dfrac14

\dfrac34

\dfrac12

Answer and worked solution

Official answer: C

P divides BC in $4:3$ : $P=\left(-\frac{20}7,-\frac{11}7\right)$ .

Lines. AP has slope $\frac23$ and meets the $x$ -axis at $-\frac12$ ; AC has slope 2 and meets it at $\frac12$ .

Area $\frac12\times1\times1=\frac12$ . (C)

Topics:Equations of a line Distance and section formulae

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JEE Main 2022 · 27 Jul · Shift 1, Mathematics question 18