Question

find the area of triangle ABC with vertices A (5, 1) B (-3, -7) C (7, -1​

Answer 1

the area of the triangle is 32 Square units

Answer 2

The area of the triangle whose vertices are  A (5, 1) B (-3, -7) C (7, -1​) is 9 square unit

Step-by-step explanation:

Given

The vertices of the triangle are:

$A(5,1), B(-3, -7), C(7, -1)$

We know that if the vertices of a triangle are $(x_1,y_1), (x_2,y_2), (x_3,y_3)$ then its area is given by

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

Therefore,

$A=\frac{1}{2}[5(-7-(-1))+(-3)(-1-1)+7(-1-(-7))]$

$\implies A=\frac{1}{2}[-30+6+42]$

$\implies A=\frac{18}{2}$

$\implies A=9$ sq unit

Hope this helps.

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