Question

Plot $(3,0),(5,0)$ and $(0,4)$ on cartesian plane. Name the figure formed by joining these points and find its area.

• A. Figure formed is a Rectangle and Area $=52$ sq. unit
• B. Figure formed is a triangle and Area $=4$ sq. unit
• C. Figure formed is a square and Area $=40$ sq. unit
• D. None of these

Answer 1

Answer: (B)

Figure formed is a triangle and Area $=4$ sq. unit

The figure is a triangle.
We know that the area of the triangle whose vertices are $(x_1,y_1),(x_2,y_2),$ and $(x_3,y_3)$ is $\frac{1}{2}\left|x_1\right(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2\left)\right|$

Therefore,

Area $=\frac{1}{2}\left[3\right(0-4)+5(4-0)+0]=4$ square units.