Question

The area of the triangle formed by the line $5x-3y+15=0$ with coordinate axes is

• A. $15c{m}^2$
• B. $5c{m}^2$
• C. $8c{m}^2$
• D. $\frac{15}{2}c{m}^2$

Answer 1

The correct option is D $\frac{15}{2}c{m}^2$

In order to find the area of triangle, we need all the coordinates of a triangle.
Draw the graph of $5x-3y=15$ on graph.
Let $x=0$,
$5\left(0\right)-3y=15$
$y=-5$
So,the first coordinate is $(0,-5)$
Now, let $y=0$,
$5x-3\left(0\right)=15$
$x=3$
So,the second coordinate is $(3,0)$ and third one is origin $(0,0)$.
Area of a triangle = $\frac{1}{2}\left(x_1\right(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2\left)\right)$= $\frac{1}{2}\left(0\right(0-0)+(3(0-5)+0(5-0))=\frac{15}{2}c{m}^2$