Find the area of the triangle formed by the three points whose coordinates are (2, 3), (4, 5) and (6, 3).Choices:- 3 sq. units 2 sq. units 4 sq units 6 sq. units
Question
Find the area of the triangle formed by the three points whose coordinates are (2, 3), (4, 5) and (6, 3).Choices:- 3 sq. units 2 sq. units 4 sq units 6 sq. units
Solution
The area of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3) is given by the formula:
Area = 1/2 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|
Substituting the given points into the formula, we get:
Area = 1/2 * |2(5 - 3) + 4(3 - 3) + 6(3 - 5)|
Solving inside the absolute value brackets, we get:
Area = 1/2 * |22 + 40 + 6*(-2)|
Area = 1/2 * |4 - 12|
Area = 1/2 * |-8|
The absolute value of -8 is 8, so:
Area = 1/2 * 8 = 4 square units
So, the area of the triangle is 4 square units.
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