# Analytic geometry - high school - math problems

#### Number of problems found: 111

- 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 - Three points

Three points K (-3; 2), L (-1; 4), M (3, -4) are given. Find out: (a) whether the triangle KLM is right b) calculate the length of the line to the k side c) write the coordinates of the vector LM d) write the directional form of the KM side e) write the d - 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 - Intersections 3

Find the intersections of the circles x^{2}+ y^{2}+ 6 x - 10 y + 9 = 0 and x^{2}+ y^{2}+ 18 x + 4 y + 21 = 0 - Points in space

There are n points, of which no three lie on one line and no four lies on one plane. How many planes can be guided by these points? How many planes are there if there are five times more than the given points? - Vector perpendicular

Find the vector a = (2, y, z) so that a⊥ b and a ⊥ c where b = (-1, 4, 2) and c = (3, -3, -1) - Angle of the body diagonals

Using vector dot product calculate the angle of the body diagonals of the cube. - Place vector

Place the vector AB, if A (3, -1), B (5,3) in the point C (1,3) so that AB = CO - Calculate 8

Calculate the coordinates of point B axially symmetrical with point A[-1, -3] along a straight line p : x + y - 2 = 0. - Find the 12

Find the equation of the circle with center (3,7) and circumference 8π units. - Vector v4

Find the vector v4 perpendicular to vectors v1 = (1, 1, 1, -1), v2 = (1, 1, -1, 1) and v3 = (0, 0, 1, 1) - Vertex points

Given the following points of a triangle: P(-12,6), Q(4,0), R(-8,-6). Graph the triangle. Find the triangle area. - A cell tower

A cell tower is located at coordinates (-5, -7) and has a circular range of 12 units. If Mr. XYZ is located at coordinates (4,5), will he be able to get a signal? - Coordinates of square vertices

I have coordinates of square vertices A / -3; 1/and B/1; 4 /. Find coordinates of vertices C and D, C 'and D'. Thanks Peter. - Three points

Three points A (-3;-5) B (9;-10) and C (2;k) . AB=AC What is value of k? - Calculate 6

Calculate the distance of a point A[0, 2] from a line passing through points B[9, 5] and C[1, -1]. - Cuboids

Two separate cuboids with different orientation in space. Determine the angle between them, knowing the direction cosine matrix for each separate cuboid. u1=(0.62955056, 0.094432584, 0.77119944) u2=(0.14484653, 0.9208101, 0.36211633) - Parametric form

Calculate the distance of point A [2,1] from the line p: X = -1 + 3 t Y = 5-4 t Line p has a parametric form of the line equation. .. - A screen

A screen is 1680 x 1050 pixels. What are the coordinates (and size in pixels) of an centered area which is exactly 33% of the screen size? - 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.

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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.