The triangle

The triangle is given by three vertices:
A [0.0]
B [-4.2]
C [-6.0]
Calculate V (intersection of heights), T (center of gravity), O - center of a circle circumscribed

Correct result:

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

Solution:

$$\begin{gathered} A=(0,0) \\ B=(-4,2) \\ C=(-6,0) \\ T=(x_1,y_1) \\ {x}_1={\displaystyle \frac{A_x+B_x+C_x}{3}}={\displaystyle \frac{0+(-4)+(-6)}{3}}=-{\displaystyle \frac{10}{3}}=-3.3333 \end{gathered}$$

$y_1={\displaystyle \frac{A_y+B_y+C_y}{3}}={\displaystyle \frac{0+2+0}{3}}={\displaystyle \frac{2}{3}}=0.6667$

$$\begin{gathered} O(x_2,y_2) \\ D=2\cdot (A_x\cdot (B_y-C_y)+B_x\cdot (C_y-A_y)+C_x\cdot (A_y-B_y))=2\cdot (0\cdot (2-0)+(-4)\cdot (0-0)+(-6)\cdot (0-2))=24 \\ {x}_2=((A_x^2+A_y^2)\cdot (B_y-C_y)+(B_x^2+B_y^2)\cdot (C_y-A_y)+(C_x^2+C_y^2)\cdot (A_y-B_y))\mathrm{/}D=((0^2+0^2)\cdot (2-0)+((-4{)}^2+2^2)\cdot (0-0)+((-6{)}^2+0^2)\cdot (0-2))\mathrm{/}24=-3 \end{gathered}$$

$y_2=((A_x^2+A_y^2)\cdot (C_x-B_x)+(B_x^2+B_y^2)\cdot (A_x-C_x)+(C_x^2+C_y^2)\cdot (B_x-A_x))\mathrm{/}D=((0^2+0^2)\cdot ((-6)-(-4))+((-4{)}^2+2^2)\cdot (0-(-6))+((-6{)}^2+0^2)\cdot ((-4)-0))\mathrm{/}24=-1$

Try another example

Showing 0 comments:

Next similar math problems:

• Center
  Calculate the coordinates of the center of gravity T [x, y] of triangle ABC; A[11,4] B[13,-7] C[-17,-18].
• Inscribed circle
  Write the equation of a incircle of the triangle KLM if K [2,1], L [6,4], M [6,1].
• Center
  In the triangle ABC is point D[1,-2,6], which is the center of the |BC| and point G[8,1,-3], which is the center of gravity of the triangle. Find the coordinates of the vertex A[x,y,z].
• Coordinates
  Determine the coordinates of the vertices and the content of the parallelogram, the two sides of which lie on the lines 8x + 3y + 1 = 0, 2x + y-1 = 0 and the diagonal on the line 3x + 2y + 3 = 0
• Centre of mass
  The vertices of triangle ABC are from the line p distances 3 cm, 4 cm and 8 cm. Calculate distance from the center of gravity of the triangle to line p.
• Center of line segment
  Calculate the distance of the point X [1,3] from the center of the line segment x = 2-6t, y = 1-4t ; t is .
• Center of gravity
  The mass points are distributed in space as follows - specify by coordinates and weight. Find the center of gravity of the mass points system: A₁ [1; -20; 3] m₁ = 46 kg A₂ [-20; 2; 9] m₂ = 81 kg A₃ [9
• Circle
  The circle touches two parallel lines p and q, and its center lies on line a, which is the secant of lines p and q. Write the equation of the circle and determine the coordinates of the center and radius. p: x-10 = 0 q: -x-19 = 0 a: 9x-4y+5 = 0
• Coordinates of the intersection of the diagonals
  In the rectangular coordinate system, a rectangle ABCD is drawn. The vertices of the rectangle are determined by these coordinates A = (2.2) B = (8.2) C = (8.6) D = (2.6) Find the coordinates of the intersection of the diagonals of the ABCD rectangle
• Coordinates of a centroind
  Let’s A = [3, 2, 0], B = [1, -2, 4] and C = [1, 1, 1] be 3 points in space. Calculate the coordinates of the centroid of △ABC (the intersection of the medians).
• Chord BC
  A circle k has the center at the point S = [0; 0]. Point A = [40; 30] lies on the circle k. How long is the chord BC if the center P of this chord has the coordinates: [- 14; 0]?
• Vertices of a right triangle
  Show that the points D(2,1), E(4,0), F(5,7) are vertices of a right triangle.
• Center
  Calculate the coordinates of the circle center: ?
• Find the 5
  Find the equation of the circle with center at (1,20), which touches the line 8x+5y-19=0
• Circle tangent
  It is given to a circle with the center S and radius 3.5 cm. Distance from the center to line p is 6 cm. Construct a circle tangent n which is perpendicular to the line p.
• Centroid - two bodies
  A body is composed of a 0.8 m long bar and a sphere with a radius of 0.1m attached so that its center lies on the longitudinal axis of the bar. Both bodies are of the same uniform material. The sphere is twice as heavy as the bar. Find the center of gravi
• Intersections 3
  Find the intersections of the circles x² + y² + 6 x - 10 y + 9 = 0 and x² + y² + 18 x + 4 y + 21 = 0