Question

What is the area of a right triangle with the given vertices? A(3,1) , B(5,4) , C(6,−1)

Answer 1

`(13)/(2)` square units

Explanation:

We are given that vertices of a right triangle are A(3,1) ,B(5,4) and C(6,-1).

We have to find the area of triangle.

We know that area of triangle=
`(1)/(2)\mid (x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2))\mid`

`x_1=3,x_2=5,x_3=6`

`y_1=1,y_2=4,y_3=-1`

Substitute the values in the formula then we get

Area of right triangle =
`(1)/(2)\mid (3(4+1)+5(-1-1)+6(1-4))\mid`

Area of right triangle =
`(1)/(2)\mid (15-10-18)\mid`

Area of right triangle =
`(1)/(2)* 13=(13)/(2)` square units