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QJEEM22Ma931b: JEE Main 2022 Mathematics - Class 11 JEEM22Ma931b Solution: Let be vertices of a triangle be a point on side , and and be…

Let A(1,1),B(−4,3),C(−2,−5)A(1,1), B(-4,3), C(-2,-5) be vertices of a triangle ABC,PA B C, P be a point on side BCB C , and Δ1\Delta_{1} and Δ2\Delta_{2} be the areas of triangles APBA P B and ABCA B C , respectively. If Δ1:Δ2=4:7\Delta_{1}: \Delta_{2}=4: 7 , then the area enclosed by the lines AP,ACA P, A C and the xx -axis is :

Multiple Choice Options

  • A 14\frac{1}{4}
  • B 34\frac{3}{4}
  • C 12\frac{1}{2}
  • D 1

Step-by-Step Verified Solution

Δ1Δ2=12×BP×AH12×BC×AH=47{{{\Delta _1}} \over {{\Delta _2}}} = {{{1 \over 2} \times BP \times AH} \over {{1 \over 2} \times BC \times AH}} = {4 \over 7}

JEE Main 2022 (Online) 27th July Morning Shift Mathematics - Straight Lines and Pair of Straight Lines Question 50 English Explanation

P(−207,−117)P\left( {{{ - 20} \over 7},{{ - 11} \over 7}} \right)

Line AC:y−1=2(x−1)AC:y - 1 = 2(x - 1)

Intersection with x-axis =(12,0)= \left( {{1 \over 2},0} \right)

Line AP:y−1=23(x−1)AP:y - 1 = {2 \over 3}(x - 1)

Intersection with x-axis (−12,0)\left( {{{ - 1} \over 2},0} \right)

Vertices are (1,1),(12,0)(1,1),\left( {{1 \over 2},0} \right) and (−12,0)\left( {{{ - 1} \over 2},0} \right)

Area =12= {1 \over 2} sq. unit

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