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Perimeter = 16.4 units
Using the heron's formula, Area ≈ 10.4 units².
<h3>What is the Heron's Formula?</h3>The heron's formula is used to find the area of a triangle with known side lengths of all its three sides, a, b, and c. The heron's formula is given as: Area = √[s(s - a)(s - b)(s - c)], where s = half the perimeter of the triangle
s = (a + b + c)/2.
Given the following:
K (-4,-1) ,
L(-2, 2),
M (3,-1)
Use the distance formula, d = , to find KL, LM, and KM.
KL = √[(−2−(−4))² + (2−(−1))²]
KL = √13 ≈ 3.6 units
LM = √[(−2−3)² + (2−(−1))²]
LM = √34 = 5.8 units
KM = √[(−4−3)² + (−1−(−1))²]
KM = √49 = 7 units
Perimeter = 3.6 + 5.8 + 7 = 16.4 units
Semi-perimeter (s) = 1/2(16.4) = 8.2 units
KL = a ≈ 3.6 units
LM = b = 5.8 units
KM = c = 7 units
s = 8.2
Plug in the values into √[s(s - a)(s - b)(s - c)]
Area = √[8.2(8.2 - 3.6)(8.2 - 5.8)(8.2 - 7)]
Area = √[8.2(4.6)(2.4)(1.2)]
Area = √108.6336
Area ≈ 10.4 units²
Learn more about heron's formula on:
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Answer:
44x +56y = 95
Step-by-step explanation:
To write the equation of the perpendicular bisector, we need to know the midpoint and we need to know the differences of the coordinates.
The midpoint is the average of the coordinate values:
((-2.5, -2) +(3, 5))/2 = (0.5, 3)/2 = (0.25, 1.5) = (h, k)
The differences of the coordinates are ...
(3, 5) -(-2.5, -2) = (3 -(-2.5), 5 -(-2)) = (5.5, 7) = (Δx, Δy)
Then the perpendicular bisector equation can be written ...
Δx(x -h) +Δy(y -k) = 0
5.5(x -0.25) +7(y -1.5) = 0
5.5x -1.375 +7y -10.5 = 0
Multiplying by 8 and subtracting the constant, we get ...
44x +56y = 95 . . . . equation of the perpendicular bisector
