Question

4. A triangle plotted in the coordinate plane has vertices at (2, 3), (sqrt15,3) and (4,8). Which of the following

is closest to its area?
(1) 4.68
(3) 7.12
(2) 5.93
(4) 8.76​

Answer 1

Option(1) is the correct answer to the given question .

Explanation:

let
`x1, y1=\ (2, 3)`

`(x2,y2)=(√(15,3) \ )`

`(x3,y3)=\ (4,8)`

Now we know that

`Area=\ (1)/(2) |x1(y2-y3)\ + \ x2(y3-y1)\ + x3(y1-y2)`

Now putting this value in the formula we get

`(1)/(2)|2(3-8)\ +√(15)(8-3)\ * 4(5-3)|`

`=\ (1)/(2)\ *9.3649`

=4.6824

Therefore option(1) is the correct answer .