Formula is:
A = | [ Ax ( B y - Cy ) + Bx ( Cy - Ay ) + Cx ( A y - By ) ] / 2 |
where:
Ax and Ay are the x and y coordinates of the point A
Bx and By are the x and y coordinates of the point B
Cx and Cy are the x and y coordinates of the point C
Two vertical bars mean "absolute value".
In this case:
Ax = - 1 , Ay = 1
Bx = - 7 , By = 1
Cx = - 3, Cy = 6
A = | [ Ax ( B y - Cy ) + Bx ( Cy - Ay ) + Cx ( A y - By ) ] / 2 |
A = | [ ( - 1 ) ∙ ( 1 - 6 ) + ( - 7 ) ∙ ( 6 - 1 ) + ( - 3 ) ( 1 - 1 ) ] / 2 |
A = | [ ( - 1 ) ∙ ( - 5 ) + ( - 7 ) ∙ ( 5 ) + ( - 3 ) ∙ 0 ) ] / 2 |
A = | ( 5 - 35 ) / 2 |
A = | - 30 / 2 |
A = | - 15 |
A = 15 units²
△ABC has vertices at A(−1,1), B(−7,1), and C(−3,6).
What is the area of △ABC?
15 units ^2
34 units ^2
35 units ^2
17 units ^2
2 answers
Notice AB is a horizontal line since A and B have the same y value
So a quick count shows AB = 6
and C(-3,6) is clearly 5 units above it, so we have the base and the height
Area = (1/2)(6)(5) = 15
This was lucky, the method Bosnian used is a general method and works for any
3 points, it is just one of many ways to do this in a general way.
So a quick count shows AB = 6
and C(-3,6) is clearly 5 units above it, so we have the base and the height
Area = (1/2)(6)(5) = 15
This was lucky, the method Bosnian used is a general method and works for any
3 points, it is just one of many ways to do this in a general way.
1 answer