Question

Find the area of the triangle whose vertices are A (1, 1), B (2, 2) and C (1, 3).​

Answer 1

Given :-

Vertices are A (1, 1), B (2, 2) and C (1, 3)

To Find :-

Area

Solution :-

We know that

$\sf Area = \dfrac{1}{2}\bigg|x_1(y_2-y_3) + x_2(y_3-y_1)+x_3(y_1 - y_2)\bigg|$

We have

x₁ = 1

x₂ = 2

x₃ = 1

y₁ = 1

y₂ = 2

y₃ = 3

$\sf Area = \dfrac{1}{2}\bigg|1(2-3) + 2(3-1)+1(1 -2 )\bigg|$

$\sf Area = \dfrac{1}{2}\bigg|1(-1) + 2(2) + 1(-1)\bigg|$

$\sf Area = \dfrac{1}{2}\bigg|-1 + 4-2\bigg|$

$\sf Area = \dfrac{1}{2}\bigg|-3 + 4\bigg|$

$\sf Area = \dfrac{1}{2}\times1$

$\sf Area = \dfrac{1}{2}$