Problem Solving

13. In the rectangular co-ordinate system, a triangle has vertices at (-6,-2), (-4,-6) and (-2,5). What is the area of the triangle?
A. 12 sq units
B. 15 sq units
C. 18 sq units
D. 21 sq units
E. 30 sq units

I dont have the OA for this question.

Hint: complete the rectanlge

13. In the rectangular co-ordinate system, a triangle has vertices at (-6,-2), (-4,-6) and (-2,5). What is the area of the triangle?
A. 12 sq units
B. 15 sq units
C. 18 sq units
D. 21 sq units
E. 30 sq units

let the co-ordinates be:

x1, y1
x2, y2 &
x3, y3

so in this problem:
x1= -6, y1 = -2
x2= -4, y2 = -6 &
x3= -2, y3 = 5

Formula; A(triangle having vertices as given above) = 1/2[x1(y2-y3)+x2(y3-y1)+x3(y1-y2)]

= 1/2[-6(-6-5)-4(5+2)-2(-2+6)]

=1/2(66-28-8)

=1/2(30)

=15

So right OA is B. 15 sq. units