Question

Area of ∆bounded by line 3x+2y+6=0 and both axes is ...... Sq unit​

Answer 1

Area of a triangle bounded by a line ax + by + c = 0 is c²/2IabI.

[ where IabI represents modulus of ab]

Here line is 3x + 2y + 6 =0

Area of triangle bounded by this line is 6²/2I3*2I = 36/12 = 3 sq units.

                       

                                              (or)

area of a triangle with vertices (x₁,y₁), (x₂,y₂) and (x₃,y₃) is

1/2 Ix₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)I  [I  I is modulus]

This line forms a triangle with one vertex as origin and the other vertices are points of intersection of this line with x axis and y axis.

this line intersects x-axis at (-2,0) and y-axis at (0,-3)

Vertices of the triangle are (0,0), (-2,0) and (0,-3)

Area of triangle is 1/2 I 0(0 - (-3)) + (-2)(-3 - 0) + 0(0 - 0) I

⇒1/2 I0 + 6 + 0I

⇒1/2 * 6

⇒ 3 sq units.