Question

The area of triangle ABC formed by A(0,5) , B(-3,0) and C(5,0) a) 10 sq. units b) 15 sq. units c) 20 sq. units d) 25 sq. units​

Answer 1

Answer:

d) 25 units²

Explanation:

Given three vertices of the triangle,

• A(0, 5)
• B(-3, 0)
• C(5, 0)

We need to calculate the area.

$\rm \longrightarrow \: Area \: of \: triangle = \dfrac{1}{2} |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|$

• Where, $\rm x_1, \: and \: y_1$ denotes the coordinates of the first point A.
• $\rm x_2, \: and \: y_2$ are the coordinates of second point B.
• $\rm x_3, \: and \: y_3$ are the coordinates of C.

By the given coordinates.

$\rm \longrightarrow \: \dfrac{1}{2} |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|$

$\rm \longrightarrow \: \dfrac{1}{2} |0(0 - 0) + ( - 3)(0 - 5) + 5(5- 0)|$

$\rm \longrightarrow \: \dfrac{1}{2} |0(0) + ( - 3)(- 5) + 5(5)|$

$\rm \longrightarrow \: \dfrac{1}{2} |0+ 15 + 25 |$

$\rm \longrightarrow \: \dfrac{1}{2} |50 |$

$\rm \longrightarrow \:25$

∴ Area of the triangle is 25 units ²