Find the area of the triangle whose vertices are (1, 2), (3, 7) and (5, 3).
Question
Find the area of the triangle whose vertices are (1, 2), (3, 7) and (5, 3).
Solution
To find the area of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), you can use the formula:
Area = 1/2 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|
Let's plug in the given points into the formula:
Area = 1/2 * |1(7 - 3) + 3(3 - 2) + 5(2 - 7)|
Simplify inside the absolute value:
Area = 1/2 * |4 + 3 - 25|
Simplify further:
Area = 1/2 * |-18|
The absolute value of -18 is 18, so:
Area = 1/2 * 18 = 9 square units.
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