Analytic geometry - practice problems - page 5 of 13
Analytic geometry, also known as coordinate geometry, is a branch of mathematics that deals with the study of geometric shapes using the techniques of calculus and algebra. It uses a coordinate system to represent geometric shapes and equations, allowing for the use of algebraic methods to solve geometric problems. It is also used to model physical phenomena, such as the motion of objects in space.Number of problems found: 248
- 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 - 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? - What is 10
What is The area of a parallelogram that has vertices with the coordinates (0, 0), (4, 0),(5, 3), and (1, 3)? - A circle
A circle relation is given to be x² + y² =16. What is the radius of the circle? - Polygon - area coordinates
Find the perimeter and the area of the polygon with the given vertices. T (2,7), U (2,9), V (5,9), W (5,7) - Quadrant four
Which point is located in Quadrant IV? A coordinate plane. A(-8, 6) B(-8, -6) C(8, -6) D(8, 6) - 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 are 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 line, rati - Quadrilateral 47493
A regular quadrilateral prism ABCDEFGH has a base edge A B 8 cm long and 6 cm high. Point M is the center of the edge AE. Determine the distance of point M from the BDH plane. - A Cartesian framework
1. In a Cartesian framework, the functions f and g we know that: The function (f) is defined by f (x) = 2x², the function (g) is defined by g (x) = x + 3, the point (O) is the origin of the reference, and point (C) is the point of intersection of the grap - CoG center
Find the position of the center of gravity of a system of four mass points having masses, m1, m2 = 2 m1, m3 = 3 m1, and m4 = 4 m1, if they lie at the vertices of an isosceles tetrahedron. (in all case - Determine 44221
For circles k1 (S1,4cm) and k2 (S2,3cm) and it holds that | S1S2 | = 8cm. Determine the distance between the circles K1 and K2. - Find quadrant
Point Y is located at (4, -2) on a graph. Point Z is located five 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 > - 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 point X on the line p so that the sum of its distances from points A and B is the smallest. - Determine
Determine which type of quadrilateral ABCD is and find its perimeter if you know the coordinates of vertices: A/2,4 /, B / -2,1 /, C / -2, -2 /, D/2, -5 /.
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