# Analytic geometry + line - practice problems

#### Number of problems found: 89

- Coordinates 65224

The line PQ is determined by points with coordinates P = [- 2; 4] and Q = [4; 0]. What are the coordinates of the center S of the line segment PQ? - 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 - Using

Using the point-slope equation, find the equation containing (-7, 3) and slope m = -4 - The coordinates

The coordinates (5, 2) and (-6, 2) are vertices of a hexagon. Explain how to find the length of the segment formed by these endpoints. How long is the segment? - 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 - 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 > - Half-planes 36831

The line p and the two inner points of one of the half-planes determined by the line p are given. Find the point X on the line p so that the sum of its distances from the points A and B is the smallest. - 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. - Determines: 33451

The line p is given by the point P [- 0,5; 1] and the direction vector s = (1,5; - 3) determines: A) value of parameter t for points X [- 1,5; 3], Y [1; - 2] lines p B) whether the points R [0,5; - 1], S [1,5; 3] lies on the line p C) parametric equations - Place vector

Place the vector AB, if A (3, -1), B (5,3) in the point C (1,3) so that AB = CO - Ascend vs. descent

Which function is growing? a) y = 2-x b) y = 20 c) y = (x + 2). (-5) d) y = x-2 - 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 - Find the 15

Find the tangent line of the ellipse 9 x² + 16 y² = 144 that has the slope k = -1 - 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]. - 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 - 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 13

Find the equation of the circle inscribed in the rhombus ABCD where A[1, -2], B[8, -3] and C[9, 4]. - 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?

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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. Line - practice problems.