22. To find the area of a triangle given the vertices, we can use the formula for the area of a triangle formed by three points (x1, y1), (x2, y2), and (x3, y3):
Area = 1/2 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|
Plugging in the coordinates:
Area = 1/2 * |-4(2 - (-3)) + 5(-3 -1) + 2(1 - 2)|
Area = 1/2 * |-4(5) + 5(-4) + 2(-1)|
Area = 1/2 * |-20 - 20 - 2|
Area = 1/2 * |-42|
Area = 21
So, the area of the triangle with vertices (-4, 1), (5, 2), and (2, -3) is 21 square units.
23. Using the same formula for the area of a triangle with vertices (-2, -3), (-5, 4), and (4, 1):
Area = 1/2 * |-2(4 - 1) + (-5)(1 - (-3)) + 4(-3 - 4)|
Area = 1/2 * |-2(3) + (-5)(4 + 3) + 4(-7)|
Area = 1/2 * |-6 + (-5)(7) + (-28)|
Area = 1/2 * |-6 + (-35) + (-28)|
Area = 1/2 * |-69|
Area = 34.5
So, the area of the triangle with vertices (-2, -3), (-5, 4), and (4, 1) is 34.5 square units.
Given the vertices, find the area of each triangle.
22. (-4,1), (5, 2), and (2, -3)
23. (-2, -3), (-5, 4), and (4, 1)
1 answer
2 answers