Center
In the ABC triangle 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].
Find the coordinates of the vertex A[x,y,z].
Correct answer:
Tips for related online calculators
The 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.
Do you have a linear equation or system of equations and looking for its solution? Or do you have a quadratic equation?
See also our trigonometric triangle calculator.
Do you have a linear equation or system of equations and looking for its solution? Or do you have a quadratic equation?
See also our trigonometric triangle calculator.
You need to know the following knowledge to solve this word math problem:
Grade of the word problem:
We encourage you to watch this tutorial video on this math problem: video1
Related math problems and questions:
- Center
Calculate the coordinates of the center of gravity T [x, y] of triangle ABC; A[-17,9] B[-26,-19] C[-7,7]. - Ratio of triangles areas
In an equilateral triangle ABC, the point T is its center of gravity, the point R is the image of the point T in axial symmetry along the line AB, and the point N is the image of the point T in axial symmetry along the line BC. Find the ratio of the areas - 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]? - Coordinates of square vertices
The ABCD square has the center S [−3, −2] and the vertex A [1, −3]. Find the coordinates of the other vertices of the square. - Isosceles triangle
In an isosceles triangle ABC with base AB; A [3,4]; B [1,6] and the vertex C lies on the line 5x - 6y - 16 = 0. Calculate the coordinates of vertex C. - Triangle midpoints
Determine coordinates of triangle ABC vertices if we know triangle sides midpoints SAB [0;3] SBC [1;6] SAC [4;5], its sides AB, BC, AC. - Center of gravity
The mass points are distributed in space as specified 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; -2; -1 - Medians 2:1
The Median to side b (tb) in triangle ABC is 12 cm long. a. What is the distance of the center of gravity T from vertex B? b, Find the distance between T and the side b. - 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 - Construction
Construct the triangle ABC if you know: the size of the side AC is 6 cm, the size of the angle ACB is 60°, and the distance of the center of gravity T from the vertex A is 4 cm. (Sketch, analysis, notation of construction, construction) - Lengths of medians from coordinates
There is a triangle ABC: A [-6.6; 1.2], B [3.4; -5.6], C [2.8; 4.2]. Calculate the lengths of its medians. - Coordinates hexagon
The regular hexagon ABCDEF is given. Point A has coordinates [1; 3], and point D has coordinates [4; 7]. Calculate the sum of the coordinates of the center of its described circle. - Rectangular 3478
A segment AB is drawn in the rectangular coordinate system with endpoints A [1;6] and B [5;2]. The center symmetry is the origin of the coordinate system. Find the coordinates of the center of this segment in this symmetry projection. - Perimeter 6002
In the triangle ABC there is a side c = 5cm and a medians ta = 6cm (median to side a), tb = 4.5cm (median to side b). Find the perimeter of the triangle ABT (T = center of gravity). - Unit vector 2D
Find coordinates of unit vector to vector AB if A[-6; 8], B[-18; 10]. - 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). - Triangle's centroid
In the triangle ABC the given lengths of its medians tc = 9, ta = 6. Let T be the intersection of the medians (triangle's centroid), and the point S is the center of the side BC. The magnitude of the CTS angle is 60°. Calculate the length of the BC side t
