Question

the area of the triangle formed by (3,-1),(2,7) and (-5,-6) is​

Answer 1

Given,

The coordinates of the three vertices of the given triangle are, (3,-1) ; (2,7) and (-5,-6).

To find,

The area of the given triangle.

Solution,

We have to apply the general formula of the area of the triangle of the coordinate geometry,in order to solve this mathematical problem.

Let,

(3,-1) = (x1,y1)

(2,7) = (x2,y2)

(-5,-6) = (x3,y3)

Now,the mathematical formula is,

Area = ½ × [x1 (y2 – y3 ) + x2 (y3 – y1 ) + x3(y1 – y2)]

= ½ × [3 (7+6) + 2 (-6+1) - 5 (-1-7)]

= ½ × ( 39 -10 +40)

= ½ × 69

= 34.5 unit²

Hence,the area of the triangle is 34.5 unit ².