Medians and sides

Determine the size of a triangle KLM and the size of the medians in the triangle. K=(-5; -6), L=(7; -2), M=(5; 6).

Correct answer:

k = 8.2462
l = 15.6205
m = 12.6491
t₁ = 13.6015
t₂ = 7.2801
t₃ = 10.7703

x_{0} = - 5 y_{0} = - 6 x_{1} = 7 y_{1} = - 2 x_{2} = 5 y_{2} = 6 k = (x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2} = (5 - 7)^{2} + (6 - (- 2))^{2} = 217 = 8.2462

l = (x_{0} - x_{2})^{2} + (y_{0} - y_{2})^{2} = ((- 5) - 5)^{2} + ((- 6) - 6)^{2} = 261 = 15.6205

m = (x_{0} - x_{1})^{2} + (y_{0} - y_{1})^{2} = ((- 5) - 7)^{2} + ((- 6) - (- 2))^{2} = 410 = 12.6491

a_{0} = (x_{1} + x_{2}) / 2 = (7 + 5) / 2 = 6 a_{1} = (y_{1} + y_{2}) / 2 = ((- 2) + 6) / 2 = 2 b_{0} = (x_{0} + x_{2}) / 2 = ((- 5) + 5) / 2 = 0 b_{1} = (y_{0} + y_{2}) / 2 = ((- 6) + 6) / 2 = 0 c_{0} = (x_{0} + x_{1}) / 2 = ((- 5) + 7) / 2 = 1 c_{1} = (y_{0} + y_{1}) / 2 = ((- 6) + (- 2)) / 2 = - 4 t_{1} = (x_{0} - a_{0})^{2} + (y_{0} - a_{1})^{2} = ((- 5) - 6)^{2} + ((- 6) - 2)^{2} = 185 = 13.6015

t_{2} = (x_{1} - b_{0})^{2} + (y_{1} - b_{1})^{2} = (7 - 0)^{2} + ((- 2) - 0)^{2} = 53 = 7.2801

t_{3} = (x_{2} - c_{0})^{2} + (y_{2} - c_{1})^{2} = (5 - 1)^{2} + (6 - (- 4))^{2} = 229 = 10.7703

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