Question

Compute the area of a triangle whose vertices are (4, 1), (1, 5), and (6, 7).

Answer 1

13 sq. units.

Explanation:

We have to calculate the area of the triangle whose vertices are (4,1), (1,5) and (6,7).

We know that the area of a triangle with vertices
`(x_(1),y_(1))`,
`(x_(2),y_(2))`, and
`(x_(3),y_(3))` is given by the formula

`(1)/(2) |x_(1)(y_(2) - y_(3)) + x_(2)(y_(3) - y_(1)) + x_(3)(y_(1) - y_(2))|`

So, the area of the given triangle will be

=
`(1)/(2)|4(5 - 7) + 1(7 - 1) + 6(1 - 5)| = 13` sq. units. (Answer)