In a two dimensional coordinate system, point A=(3,6), point B=(1,1) and point C=(7,6). Find the area?
Is there a trick to this question for me to able to do this on the Real DAT QUICK?
This one's been answered 10 billion times but I'll do it again.
Since A and C are on the same horizontal line (y-coord is 6), that can be the base. So the base is 7 - 3 = 4 units. The height goes from the base to the y-coordinate of point B. So that's 6 - 1 = 5 units. So use A = 1/2 * b * h = 1/2 * 4 * 5 = 10 units^2.
Alternatively, had the base NOT been so easy to figure out:
First normalize it so that one point is at the origin. You can do that by subtracting 1 from each coordinate so you have:
A = (2, 5); B = (0, 0); C = (6,5).
Now since you have a point at (0,0), it's as though you have two vectors leading to [2, 5] and [6, 5]. To find area you compute the determinate:
6, 5
2, 5
Area = 1/2 * [(6)(5) - (5)(2)] = 1/2*20 = 10.
The 6*5 is the 6 multiplied by the lower-right 5. The 5*2 is the upper-right 5 multiplied by the 2.
If you had put the 2, 5 on top you'd have gotten (-10) and since area is positive you'd simply have 10 as your answer.
The determinate of two vectors is the area of the parallelogram they form so that's why you divide it by 2 to find the area of the triangle.
