1. Tardigrade
  2. Question
  3. Mathematics
  4. 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.

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Q. 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.

Straight Lines

Solution:

$L _{1}: y = x +2, $
$L _{2}: x + y =2$
image
$\therefore $ Area $(\Delta ABC )=\frac{1}{2}(4)(2)=4$