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1. Find th area of the triangle formed by the points located at ( 5, 2) , (-9, -3) and (-3, -5).
- A. 27 square unit
- B. 27 square unit
- C. 27 square unit
- D. 27 square unit
Answer: Option B
Explanation:
The shoelace formula for finding the area of a triangle given its vertices (x1, y1), (x2, y2), and (x3, y3) is:
Area = 1/2 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|
In this case, the three points are: A(5, 2) B(-9, -3) C(-3, -5)
Plug these coordinates into the formula:
Area = 1/2 * |5(-3 - (-5)) + (-9)(-5 - 2) + (-3)(2 - (-3))|
Simplify the expression inside the absolute value:
Area = 1/2 * |5(2) + (-9)(-7) + (-3)(5)|
Area = 1/2 * |10 + 63 - 15|
Area = 1/2 * |58|
Area = 29 square units
So, the area of the triangle formed by the points (5, 2), (-9, -3), and (-3, -5) is 29 square units.
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