To find the area of a triangle where you know the x and y coordinates of the three vertices, you'll need to use the coordinate geometry formula: area = the absolute value of Ax(By - Cy) + Bx(Cy - Ay) + Cx(Ay - By) divided by 2. Ax and Ay are the x and y coordinates for the vertex of A. The same applies for the x and y notations of the B and C vertices.
To express absolute value, use two vertical lines, one on each side of the formula.
Fill in the numbers for each corresponding letter combination within the formula. For example, if the coordinates of the triangle's vertices are A: (13,14), B: (16, 30) and C: (50, 10), where the first number is the x coordinate and the second is y, fill in your formula like this: 13(30-10) + 16(10-14) + 50(14-30).
Subtract the numbers within the parentheses. In this example, subtracting 10 from 30 = 20, 14 from 10 = -4 and 30 from 14 = -16.
Multiply that result by the number to the left of the parentheses. In this example, multiplying 13 by 20 = 260, 16 by -4 = -64 and 50 by -16 = -800.
Add the three products together. In this example, 260 + (-64) + (-800) to get -604.
Divide the sum of the three products by 2. In this example, -604 / 2 = -302.
Remove the negative sign (-) from the number 302. The area of the triangle is 302, found from the three vertices. Because the formula calls for absolute value, you simply remove the negative sign.
- To express absolute value, use two vertical lines, one on each side of the formula.
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