# 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).

Result

x =  1.667
y =  0.333
z =  1.667

#### Solution:

$x_{0}=3 \ \\ y_{0}=2 \ \\ z_{0}=0 \ \\ \ \\ x_{1}=1 \ \\ y_{1}=-2 \ \\ z_{1}=4 \ \\ \ \\ x_{2}=1 \ \\ y_{2}=1 \ \\ z_{2}=1 \ \\ \ \\ x=\dfrac{ x_{0}+x_{1}+x_{2} }{ 3 }=\dfrac{ 3+1+1 }{ 3 } \doteq \dfrac{ 5 }{ 3 } \doteq 1.6667 \doteq 1.667$
$y=\dfrac{ y_{0}+y_{1}+y_{2} }{ 3 }=\dfrac{ 2+(-2)+1 }{ 3 } \doteq \dfrac{ 1 }{ 3 } \doteq 0.3333 \doteq 0.333$
$z=\dfrac{ z_{0}+z_{1}+z_{2} }{ 3 }=\dfrac{ 0+4+1 }{ 3 } \doteq \dfrac{ 5 }{ 3 } \doteq 1.6667 \doteq 1.667$

Try calculation via our triangle calculator.

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 0 comments:
Be the first to comment!

Tips to related online calculators
Looking for help with calculating arithmetic mean?
For Basic calculations in analytic geometry is helpful line slope calculator. From coordinates of two points in the plane it calculate slope, normal and parametric line equation(s), slope, directional angle, direction vector, the length of segment, intersections the coordinate axes etc.
Looking for a statistical calculator?
Two vectors given by its magnitudes and by included angle can be added by our vector sum calculator.
See also our trigonometric triangle calculator.

## Next similar math problems:

1. Circular railway
The railway is to interconnect in a circular arc the points A, B, and C, whose distances are | AB | = 30 km, AC = 95 km, BC | = 70 km. How long will the track from A to C?
2. Trapezoid MO
The rectangular trapezoid ABCD with right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other. Calculate the perimeter and area of ​​the trapezoid.
3. Eq triangle minus arcs
In an equilateral triangle with a 2cm side, the arcs of three circles are drawn from the centers at the vertices and radii 1cm. Calculate the content of the shaded part - a formation that makes up the difference between the triangle area and circular cuts
4. Area of a rectangle
Calculate the area of a rectangle with a diagonal of u = 12.5cm and a width of b = 3.5cm. Use the Pythagorean theorem.
5. Ratio of sides
Calculate the area of a circle that has the same circumference as the circumference of the rectangle inscribed with a circle with a radius of r 9 cm so that its sides are in ratio 2 to 7.
6. Circular ring
Square with area 16 centimeters square are inscribed circle k1 and described circle k2. Calculate the area of circular ring, which circles k1, k2 form.
7. Hexagonal pyramid
Calculate the surface area of a regular hexagonal pyramid with a base inscribed in a circle with a radius of 8 cm and a height of 20 cm.
8. Squares above sides
Two squares are constructed on two sides of the ABC triangle. The square area above the BC side is 25 cm2. The height vc to the side AB is 3 cm long. The heel P of height vc divides the AB side in a 2: 1 ratio. The AC side is longer than the BC side. Calc
9. Trapezoid MO-5-Z8
ABCD is a trapezoid that lime segment CE divided into a triangle and parallelogram as shown. Point F is the midpoint of CE, DF line passes through the center of the segment BE and the area of the triangle CDE is 3 cm2. Determine the area of the trapezoid
10. Rectangle
In rectangle with sides, 6 and 3 mark the diagonal. What is the probability that a randomly selected point within the rectangle is closer to the diagonal than to any side of the rectangle?
11. The trapezium
The trapezium is formed by cutting the top of the right-angled isosceles triangle. The base of the trapezium is 10 cm and the top is 5 cm. Find the area of trapezium.
12. Annular area
The square with side a = 1 is inscribed and circumscribed by circles. Find the annular area.
13. Quarter circle
What is the radius of a circle inscribed in the quarter circle with a radius of 100 cm?
14. Quadrilateral 2
Show that the quadrilateral with vertices P1(0,1), P2(4,2) P3(3,6) P4(-5,4) has two right triangles.
15. 30-gon
At a regular 30-gon the radius of the inscribed circle is 15cm. Find the "a" side size, circle radius "R", circumference, and content area.
16. Company logo
The company logo consists of a blue circle with a radius of 4 cm, which is an inscribed white square. What is the area of the blue part of the logo?
17. The sides 2
The sides of a trapezoid are in the ratio 2:5:8:5. The trapezoid’s area is 245. Find the height and the perimeter of the trapezoid.