# Analytic geometry - high school - practice problems

#### Number of problems found: 124

- Three

Three points are given: A (-3, 1), B (2, -4), C (3, 3) a) Find the perimeter of triangle ABC. b) Decide what type of triangle the triangle ABC is. c) Find the length of the inscribed circle - 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. - What is 19

What is the equation of the line whose x - intercept is - 3 and y - intercept is -4? Find coefficients A, B, C in normal line equation: Ax + By = C - A circle

A circle relation is given to be x² + y² =16. What is the radius of the circle? - Luiza

Luiza delivers newspapers in her neighborhood. If you plot the points (-1, 1), (4, 1), (4, -2) and (-1, -2), you will create a representation of the route she takes, in miles. How many miles does her route cover? - Construct 8

Construct an analytical geometry problem where it is asked to find the vertices of a triangle ABC: the vertices of this triangle must be the points A (1,7) B (-5,1) C (5, -11). the said problem should be used the concepts of: distance from a point to a li - A Cartesian framework

1. In a Cartesian framework, the functions f and g we know that: the function (f) is defined by f (x) = 2x ^ 2, the function (g) is defined by g (x) = x + 3, the point (O) is the origin of the reference, point (C) is the point of intersection of the graph - CoG center

Find the position of the center of gravity of a system of four mass points having masses, m_{1}, m_{2}= 2 m1, m_{3}= 3 m1, and m_{4}= 4 m_{1}, if they lie at the vertices of an isosceles tetrahedron. (in all case - Find quadrant

On a graph, Point Y is located at (4, -2). Point Z is located 5 units to the left of Point Y. In which quadrant is Point Z located? - Tangens parallelogram

If ∠BAD between the sides AB and AD of the parallelogram is θ, what is tan θ? See diagram: A=(7,1) B=(5,-2) C=(12,1) D=(14,4) - Parametric equation

Point A [6; -2]. Point B = [-3; 1] Write the parametric equation of the line BA so that t belongs to the closed interval < 0;3 > - Perpendicular projection

Determine the distance of a point B[1, -3] from the perpendicular projection of a point A[3, -2] on a straight line 2 x + y + 1 = 0. - 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. - Place vector

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

In all examples, write the GENERAL EQUATION OF a line that is given in some way. A) the line is given parametrically: x = - 4 + 2p, y = 2 - 3p B) the line is given by the slope form: y = 3x - 1 C) the line is given by two points: A [3; -3], B [-5; 2] D) t - Tangents to ellipse

Find the magnitude of the angle at which the ellipse x² + 5 y² = 5 is visible from the point P[5, 1]. - 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 - There

There is a triangle ABC: A (-2,3), B (4, -1), C (2,5). Determine the general equations of the lines on which they lie: a) AB side, b) height to side c, c) Axis of the AB side, d) median ta to side a - 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. - 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

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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. Analytic geometry - practice problems. Examples for secondary school students.