Find the area of the triangle formed by the line 4 x-5 y+20=0 with the coordinate axes.

Question

Find the area of the triangle formed by the line 4 x-5 y+20=0 with the coordinate axes. (A) 1 mathrmsq. units (B) 5 mathrmsq. units (C) 10 mathrmsq. units (D) 20 mathrmsq. units

Tardigrade Admin · Accepted Answer

text Given: 4 x-5 y+20=0 ⇒ 4 x-5 y=-20 ⇒ (4 x/-20)-(5 y/-20)=1 ⇒ (x/-5)+(y/4)=1 a=-4, b=5 Area of triangle =|(a ⋅ b/2)|=|((-4) ⋅(5)/2)|=10 text sq. units

Q. Find the area of the triangle formed by the line $4 x - 5 y + 20 = 0$ with the coordinate axes.

$1 sq$ . units

$5 sq$ . units

$10 sq$ . units

$20 sq$ . units

$Given: 4 x - 5 y + 20 = 0$
$\Rightarrow 4 x - 5 y = - 20$
$\Rightarrow \frac{4 x}{- 20} - \frac{5 y}{- 20} = 1 \Rightarrow \frac{x}{- 5} + \frac{y}{4} = 1$
$a = - 4, b = 5$
Area of triangle
$= ∣ ∣ \frac{a \cdot b}{2} ∣ ∣ = ∣ ∣ \frac{( - 4 ) \cdot ( 5 )}{2} ∣ ∣ = 10 sq. units$

Q. Find the area of the triangle formed by the line 4x−5y+20=0 with the coordinate axes.

1sq. units

5sq. units

10sq. units

20sq. units