Coordinates 32183

The triangle ABC is given in the plane. A (-3,5), B (2,3), C (-1, -2) write the coordinates of the vectors u, v, w if u = AB, v = AC, w = BC. Enter the coordinates of the centers of the lines SAB (..), SAC (...), SBC (. ..)

Correct answer:

u₀ = 5
u₁ = -2
v₀ = 2
v₁ = -7
w₀ = -3
w₁ = -5
x₀ = -0.5
y₀ = 4
x₁ = -2
y₁ = 1.5
x₂ = 0.5
y₂ = 0.5

Step-by-step explanation:

A_{0} = - 3; A_{1} = 5 B_{0} = 2; B_{1} = 3 C_{0} = - 1; C_{1} = - 2 u = (u_{0}, u_{1}) = A B = B - A u_{0} = B_{0} - A_{0} = 2 - (- 3) = 5

u_{1} = B_{1} - A_{1} = 3 - 5 = - 2

v = (v_{0}, v_{1}) = A C = C - A v_{0} = C_{0} - A_{0} = (- 1) - (- 3) = 2

v_{1} = C_{1} - A_{1} = (- 2) - 5 = - 7

w = (w_{0}, w_{1}) = B C = C - B w_{0} = C_{0} - B_{0} = (- 1) - 2 = - 3

w_{1} = C_{1} - B_{1} = (- 2) - 3 = - 5

S_{0} = (x_{0}, y_{0}) = A B / 2 x_{0} = (A_{0} + B_{0}) / 2 = ((- 3) + 2) / 2 = - 0.5

y_{0} = (A_{1} + B_{1}) / 2 = (5 + 3) / 2 = 4

S_{1} = (x_{1}, y_{1}) = A C / 2 x_{1} = (A_{0} + C_{0}) / 2 = ((- 3) + (- 1)) / 2 = - 2

y_{1} = (A_{1} + C_{1}) / 2 = (5 + (- 2)) / 2 = 1.5

S_{2} = (x_{2}, y_{2}) = B C / 2 x_{2} = (B_{0} + C_{0}) / 2 = (2 + (- 1)) / 2 = 0.5

y_{2} = (B_{1} + C_{1}) / 2 = (3 + (- 2)) / 2 = 0.5

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