Question

Area of a Triangle Find the area of the triangle formed by the coordinate axes and the line

$2y+3x-6=0$

Short answer

The area of a triangle is 3 units².

Step-by-step solution

Step 1. Concept of area of a triangle.

The area of a triangle determine by its multiplication of base and height and divided by 2.

Step 2. Determine x and y-intercept of line.

The given equation is $2y+3x-6=0\cdots \left(1\right).$

x-Intercept: Substitute $y=0$in equation (1).

localid="1646052753653" $x=2$

y-Intercept: Substitute width="36">x=0in equation (1).

$y=3$

Hence, the line cuts the coordinate axes at$\left(2,0\right)$and $\left(0,3\right)$.

Step 3. Determine the area of a triangle.

Since, the line (1) cut the y-axis at 3 hence, the height of a triangle is 3 unit and the line (1) cut the x-axis at 2 hence, the base of a triangle is 2 unit.

Area of triangle $$\begin{gathered} =\frac{1}{2}\times \mathrm{Area}\mathrm{of}\mathrm{base}\times \mathrm{height} \\ =\frac{1}{2}\times 2\times 3{\mathrm{unit}}^2 \\ =3{\mathrm{unit}}^2. \end{gathered}$$