Question

find the area of the triangle ABC whose vertices are A(2, 3), B(-1, 2) and C(2, -4)​

Answer 1

Answer :

10.5units²

Explanation :

Given vertices of a triangle ABC :-

• A(2, 3)
• B(-1, 2)
• C(2, -4)

Find the area of the triangle.

Formula to be used :

${ \longrightarrow{\rm {\dfrac{1}{2}\big[x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \big]}}}$

Here,

• $\rm x_1 = 2\: and\: y_1 = 3$
• $\rm x_2 = -1\: and\: y_2 = 2$
• $\rm x_3 = 2\: and\: y_3 = -4$

On substituting the values,

$\rm \longrightarrow \: \dfrac{1}{2} \big[2 \big(2 - ( - 4) \big) + ( - 1) \big(- 4 - 3 \big) + 2(3 - 2)\big]$

$\rm \longrightarrow \: \dfrac{1}{2} [2(4 + 2) - 1( - 7) + 2]$

$\rm \longrightarrow \: \dfrac{1}{2} [2(6) + 7 + 2]$

$\rm \longrightarrow \: \dfrac{1}{2}[12 + 5]$

$\rm \longrightarrow \: \dfrac{1}{2} [21]$

$\rm \longrightarrow \orange{ 10.5 \: units^{2}}$

Required answer : 10.5units²