# Find the area of the triangle whose vertices are $(-8,4),(-6,6)$ and $(-3,9)$.

#### Complete Python Prime Pack

9 Courses     2 eBooks

#### Artificial Intelligence & Machine Learning Prime Pack

6 Courses     1 eBooks

#### Java Prime Pack

9 Courses     2 eBooks

Given:

Vertices of a triangle are $(-8,4),(-6,6)$ and $(-3,9)$.

To do:

We have to find the area of the given triangle.

Solution:

Let $A(-8, 4), B(-6, 6)$ and $C(-3, 9)$ be the vertices of a $\triangle ABC$.

We know that,

Area of a triangle with vertices $(x_1,y_1), (x_2,y_2), (x_3,y_3)$ is given by,

Area of $\Delta=\frac{1}{2}[x_{1}(y_{2}-y_{3})+x_{2}(y_{3}-y_{1})+x_{3}(y_{1}-y_{2})]$

Therefore,

Area of triangle $ABC=\frac{1}{2}[-8(6-9)+(-6)(9-4)+(-3)(4-6)]$

$=\frac{1}{2}[-8(-3)+(-6)(5)+(-3)(-2)]$

$=\frac{1}{2}[24-30+6]$

$=\frac{1}{2} \times 0$

$=0$ sq. units.

The area of the given triangle is $0$ sq. units.

Updated on 10-Oct-2022 13:28:51