The triangle

Three vertices give the triangle:
A [0.0]
B [-4.2]
C [-6.0]
Calculate V (intersection of heights), T (center of gravity), O - the center of a circle circumscribed

Correct answer:

x₁ = -3.3333
y₁ = 0.6667
x₂ = -3
y₂ = -1

Step-by-step explanation:

A = (0, 0) B = (- 4, 2) C = (- 6, 0) T = (x_{1}, y_{1}) x_{1} = \frac{A _{x} + B _{x} + C _{x}}{3} = \frac{0 + ( - 4 ) + ( - 6 )}{3} = - \frac{1 0}{3} = - 3 \frac{1}{3} = - 3.3333

y_{1} = \frac{A _{y} + B _{y} + C _{y}}{3} = \frac{0 + 2 + 0}{3} = \frac{2}{3} = 0.6667

O (x_{2}, y_{2}) D = 2 \cdot (A_{x} \cdot (B_{y} - C_{y}) + B_{x} \cdot (C_{y} - A_{y}) + C_{x} \cdot (A_{y} - B_{y})) = 2 \cdot (0 \cdot (2 - 0) + (- 4) \cdot (0 - 0) + (- 6) \cdot (0 - 2)) = 24 x_{2} = ((A_{x}^{2} + A_{y}^{2}) \cdot (B_{y} - C_{y}) + (B_{x}^{2} + B_{y}^{2}) \cdot (C_{y} - A_{y}) + (C_{x}^{2} + C_{y}^{2}) \cdot (A_{y} - B_{y})) / D = ((0^{2} + 0^{2}) \cdot (2 - 0) + ((- 4)^{2} + 2^{2}) \cdot (0 - 0) + ((- 6)^{2} + 0^{2}) \cdot (0 - 2)) / 24 = - 3

y_{2} = ((A_{x}^{2} + A_{y}^{2}) \cdot (C_{x} - B_{x}) + (B_{x}^{2} + B_{y}^{2}) \cdot (A_{x} - C_{x}) + (C_{x}^{2} + C_{y}^{2}) \cdot (B_{x} - A_{x})) / D = ((0^{2} + 0^{2}) \cdot ((- 6) - (- 4)) + ((- 4)^{2} + 2^{2}) \cdot (0 - (- 6)) + ((- 6)^{2} + 0^{2}) \cdot ((- 4) - 0)) / 24 = - 1

Did you find an error or inaccuracy? Feel free to write us. Thank you!

Tips for related online calculators

Looking for help with calculating arithmetic mean?
Line slope calculator is helpful for basic calculations in analytic geometry. The coordinates of two points in the plane calculate slope, normal and parametric line equation(s), slope, directional angle, direction vector, the length of the segment, intersections of the coordinate axes, etc.
Looking for a statistical calculator?
See also our trigonometric triangle calculator.