Question

1. Find the area of the triangle whose vertices are respectively,
(i) (3, 0), (-2, 1) and (-1, - 2)​

Answer 1

Step-by-step explanation:

area of triangle =1/2[x1(y3-y2)+x2(y2-y1)+x3(y1-y2)]

Answer 2

Given :

Coordinates of vertices are ;

• (3,0),(-2,1) and (-1,-2).

To Find :

• Area of the traingle

Formula used :

$Area \: of \: triangle = \frac{1}{2} \times| x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|$

Solution:

Let us consider,the respective coordinates is of traingle ABC,then

A(3,0) → (x1,y1)

B(-2,1) → (x2,y2)

C(-1,-2) → (x3,y3)

Hence,

$Area \: of \: triangle = \frac{1}{2} \times |3(1 + 2) - 2( - 2 - 0) - 1(0 - 1)| \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{1}{2} \times |3(3) - 2( - 2) - 1( - 1)| \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{1}{2} \times |9 + 4 + 1 |\\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{1}{2} \times| 14 |\\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 7 \: square \: units$

Therefore,the area of the traingle is 7 Square units.