The equations of the three perpendicular bisectors in the triangle ABC are y = - (1 / 2) · x + 9 / 4, x = 2 and y = - (6 / 7) · x + 24 / 7.
Triangles are polygons with three sides and three perpendicular bisectors, whose equations need the informations of slopes and midpoints of each side. Bisectors are lines that partitions line segments in two parts of equal length.
First, determine the midpoints of each side:
Side AB
M₁(x, y) = 0.5 · (- 3, 0) + 0.5 · (0, 6)
M₁(x, y) = (- 1.5, 0) + (0, 3)
M₁(x, y) = (- 1.5, 3)
Side BC
M₂(x, y) = 0.5 · (0, 6) + 0.5 · (4, 6)
M₂(x, y) = (0, 3) + (2, 3)
M₂(x, y) = (2, 6)
Side AC
M₃(x, y) = 0.5 · (- 3, 0) + 0.5 · (4, 6)
M₃(x, y) = (- 1.5, 0) + (2, 3)
M₃(x, y) = (0.5, 3)
Second, determine the slope of the perpendicular bisectors:
Side AB
m = (6 - 0) / [0 - (- 3)]
m = 2
m' = - 1 / m
m' = - 1 / 2
Side BC
m = (6 - 6) / (4 - 0)
m = 0
m' = - 1 / m
m' = NaN (Vertical line)
Side AC
m = [4 - (-3)] / (6 - 0)
m = 7 / 6
m' = - 1 / (7 / 6)
m' = - 6 / 7
Third, derive the equations of the bisectors:
Side AB
b = 3 - (- 1 / 2) · (- 1.5)
b = 9 / 4
y = - (1 / 2) · x + 9 / 4
Side BC
x = 2
Side AC
b = 3 - (- 6 / 7) · (0.5)
b = 24 / 7
y = - (6 / 7) · x + 24 / 7
The equations of the three perpendicular bisectors in the triangle ABC are y = - (1 / 2) · x + 9 / 4, x = 2 and y = - (6 / 7) · x + 24 / 7.
To learn more on bisectors: https://brainly.com/question/13880193
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