Straight line L 1 is parallel to the bisector of first and third quadrant, forms a triangle of area 2 square units with coordinate axes in second quadrant. Line L 2 passes throuth M (1,1) and has positive x and y intercepts. L 2 makes a triangle of minimum area with coordinates axes. Find the area of triangle formed by L 1, L 2 and x-axis.

Question

Straight line L 1 is parallel to the bisector of first and third quadrant, forms a triangle of area 2 square units with coordinate axes in second quadrant. Line L 2 passes throuth M (1,1) and has positive x and y intercepts. L 2 makes a triangle of minimum area with coordinates axes. Find the area of triangle formed by L 1, L 2 and x-axis. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

L 1: y = x +2, L 2: x + y =2 <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/001f7ceaad705b092cfa9a9731fa96fa-.png" /> ∴ Area (Δ ABC )=(1/2)(4)(2)=4

L1​:y=x+2, L2​:x+y=2 ∴ Area (ΔABC)=21​(4)(2)=4

$L_{1} : y = x + 2,$
$L_{2} : x + y = 2$

$∴$ Area $(Δ A BC) = \frac{1}{2} (4) (2) = 4$