Question

Find the area of triangle whose vertices are(- 8, -2), (-4, -6) and (- 1, 5)​

Answer 1

Step-by-step explanation:

hope it helps you and Yes pls verify the answer

Answer 2

Given,

Vertices of triangle, $\[ = \left( { - 8, - 2} \right),\left( { - 4, - 6} \right),\left( { - 1,5} \right)\]$

Solution,

Know that if vertices of triangle are $\[\left( {{x_1},{y_1}} \right),\left( {{x_2},{y_2}} \right),\left( {{x_3},{y_3}} \right)\]$. The area of triangle is $\[\frac{1}{2}\left\{ {{x_1}\left( {{y_2} - {y_3}} \right) + {x_2}\left( {{y_3} - {y_1}} \right) + {x_3}\left( {{y_1} - {y_2}} \right)} \right\}\]$

Calculate the area,

$\[ = \frac{1}{2}\left\{ {{x_1}\left( {{y_2} - {y_3}} \right) + {x_2}\left( {{y_3} - {y_1}} \right) + {x_3}\left( {{y_1} - {y_2}} \right)} \right\}\]$

$\[ = \frac{1}{2}\left\{ {\left( { - 8} \right)\left( { - 6 - 5} \right) + \left( { - 4} \right)\left( {5 + 2} \right) + \left( { - 1} \right)\left( {\left( { - 2} \right) - \left( { - 6} \right)} \right)} \right\}\]$

$\[ = \frac{1}{2}\left\{ {\left( { - 8} \right) \times \left( { - 11} \right) + \left( { - 4} \right) \times 7 + \left( { - 1} \right) \times \left( 4 \right)} \right\}\]$

$\[ = \frac{1}{2}\left\{ {88 - 28 - 4} \right\}\]$

$\[ = 28\]$

Hence the area of triangle is $\[28\,uni{t^2}\]$.