Question

$\text{Draw the graph generated by the equation}\;\; \frac{x}{3}+\frac{y}{4} =1. \\\text{Determine the area of the triangle produced by the drawn line and the coordinate axes}$

Answer 1

Given :-

Equation is x/3 + y/4 = 1

To find :-

Area of the triangle formed with coordinate axis of the given line.

Solution :-

We are given,

⇒ x/3 + y/4 = 1

Multiply this equation with 12

⇒ 4x + 3y = 12

Now, if we substitute x = 0, we get :

⇒ 4(0) + 3y = 12

⇒ 3y = 12

⇒ y = 12/3

⇒ y = 4

If we substitute y = 0 , we get :

⇒ 4x + 3(0) = 12

⇒ 4x = 12

⇒ x = 12/4

⇒ x = 3

Now we get two coordinates on the given line which are enough to plot the graph.

• ( 3, 0)
• ( 0, 4)

[See the graph in attachment.]

The vertices of the triangle formed are (3,0) , (0,4) and (0,0)

Assume the coordinates as :-

• (3,0) = (x1 , y1)
• (0,4) = (x2, y2)
• (0,0) = (x3, y3)

Area of the triangle is given by,

⇒ Ar. ∆ = 1/2 | x1(y2-y3)+ x2(y3-y1) +x3(y1-y3) |

⇒ Ar. ∆ = 1/2 | 3(4-0) + 0(0-0) + 0(0-0) |

⇒ Ar. ∆ = 1/2 | 12 |

⇒Ar. ∆ = 1/2 × 12

⇒ Ar. ∆ = 6

Hence the area of the given triangle is 6 unit square.