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

JEE Main 2022 Mathematics question

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

(1)1/4
(2)3/4
(3)1/2Correct
(4)1

Answer: (3)

Solution

Since the triangles APB and ABC have the same height from A, = BP/BC = 4/7. So P divides BC in the ratio 4 : 3 and P = (−20/7, −11/7). The line AC: y − 1 = 2(x − 1) meets the x-axis at (1/2, 0).

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Question ID VK-034433