Question

Draw the graph representing the equations x - y = 1 and 2x + 3y = 12 on the same

graph paper. Find the area of the triangles formed by these lines, the X-axis and

the Y-axis​

Answer 1

Answer:

Equation 1:

• x - y = 1

⇒ x = y

Considering some points for plotting, we get:

If x = 0, y = 0

If x = 1, y = 1

If x = 3, y = 3

Hence the required points for plotting Eqn. 1 line are:

• (0,0) (1,1) and (3,3)

Equation 2:

• 2x + 3y = 12

⇒ 2x = 12 - 3y

⇒ x = (12 - 3y) / 2

Finding the required points for plotting we get:

If y = 0, then x is:

⇒ x = (12 - 0) / 2 = 6

If y = 1, then x is:

⇒ x = ( 12 - 3(1) ) / 2

⇒ x = ( 12 - 3 ) / 2 = 4.5

If y = 4, then x is:

⇒ x = ( 12 - 3(4) ) / 2

⇒ x = ( 12 - 12 ) / 2

⇒ x = 0 / 2 = 0

Hence the required points for plotting Eqn. 2 line are:

• (6,0), (4.5,1) and (0,4)

(Refer to the attachment for the graph.)

Now we are required to find the area of the triangle. (Yellow Part)

We know that,

Area of triangle = 0.5 × Base × Height

From the diagram we can see that the top vertex is having a coordinate (2.4, 2.4). Therefore the distance of top vertex from x-axis is 2.4 units, which is the height of the triangle.

Similarly, the base of the triangle is from (0,0) to (6,0). Hence the base length is 6 units. Therefore,

⇒ Area of triangle = 0.5 × 6 × 2.4

⇒ Area of triangle = 7.2 sq. units.

Hence the area of the triangle is 7.2 sq. units.