Question

The area of triangle whose vertices are at the point (-3,1),(1,-3) and (2,3) is …….
1 point
A)15sq.units
B)25sq.units
C)24sq.units
D)14 sq.units​

Answer 1

Given:

The vertices of a triangle are ( -3 , 1 ) , ( 1 ,-3 ) and ( 2 , 3 )

To find :

The area of triangle.

Formula to be used:

Area of triangle = $\frac{1}{2} [x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)]$

Solution:

We can find the area of a triangle by using the following formula,

Area of triangle = $\frac{1}{2} [x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)]$

Let,

$x_1 = -3 , y_1 = 1 \\\x_2 = 1 , y_2 = -3\\\x_3= 2,y_3 = 3$  

Area of triangle = $\frac{1}{2} [-3(-3-3)+1(3-1)+2(1-(-3))]$

Area of triangle = $\frac{1}{2} [-3(-6)+1(2)+2(4))]$

Area of triangle = $\frac{1}{2} [18+2+8]$

Area of triangle = $\frac{1}{2} [28]$

Area of triangle = 14 sq.units

Final answer:

The area of triangle whose vertices are at the point ( -3 , 1 ) , ( 1 ,-3 ) and

( 2 , 3 ) is 14 sq.units

Thus, the correct option is D) 14 sq.units