Question

Draw the graph of two lines whose equations are 3x-2y+6=0 and x+2y-6=0 on the same graph paper.Find the area of the triangle formed by the two lines and the x-axis.​

Answer 1

SOLUTION:-

Refer all Attachment.

The triangle so formed by equation of line and x axis you can see.

coordinates of points

A = (x1,y1) = (0,3)

B = (x2 ,y2) = (6,0)

C = (x3, y3) = (-2, 0)

D = (x, y) = (0,0) coordinate of origin.

•°• The distance of AD from origin is 3unit.

•°• AD = 3 .....(1)

now,

By distance Formula

d(B,C) = √((x3 - x2)² + (y3 - y2)²)

= √((-2 - 6))² + (0 - 0)²)

= √((-8)² + 0)

= √(64)

= 8

d(B, C) = 8 unit

•°• BC = 8 ....(2)

Now,

Area of triangle so formed = 1/2 × AD × BC

= 1/2 × 3 × 8

= 4 × 3

= 12sq unit

The area of the triangle formed by the two lines and the x-axis 12 sq unit