Analytic geometry - math word problems - page 10 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
- Rectangle 39
Find the perimeter and area of the rectangular with vertices (-1, 4), (0,4), (0, -1), and (-4, 4) - Points on line segment
Points P and Q belong to segment AB. If AB=a, AP = 2PQ = 2QB, find the distance between point A and the midpoint of segment QB. - Right angled triangle 2
LMN is a right-angled triangle with vertices at L(1,3), M(3,5), and N(6,n). Given angle LMN is 90° find n - Quadrilateral 2
Show that the quadrilateral with vertices P1(0,1), P2(4,2), P3(3,6) P4(-5,4) has two right triangles.
- Vertices of RT
Show that the points P1 (5,0), P2 (2,1) & P3 (4,7) are the vertices of a right triangle. - Calculate 4865
Calculate the length of the line segment AB, given A [8; -6] and B [4; 2] - Ladder
A 4 m long ladder touches the cube 1mx1m at the wall. How high reach on the wall? - Cuboids
Two separate cuboids with different orientations are 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) - Medians and sides
Triangle ABC in the plane Oxy; are the coordinates of the points: A = 2.7 B = -4.3 C-6-1 Try to calculate the lengths of all medians and all sides.
- Resultant force
Calculate mathematically and graphically the resultant of three forces with a common center if: F1 = 50 kN α1 = 30° F2 = 40 kN α2 = 45° F3 = 40 kN α3 = 25° - Three vectors
The three forces whose amplitudes are in ratio 9:10:17 act in the plane at one point to balance. Determine the angles of each two forces. - Circle - AG
Find the coordinates of the circle and its diameter if its equation is: x² + y² - 6x-4y=36 - Equation of circle
Find an equation of the circle with indicated properties: a. center at (-3,5), diameter 20. b. center at origin and diameter 16. - Intersection 3486
The rectangular coordinate system has a point A [-2; -4] and a point S [0; -2]. Determine the coordinates of points B, C, and D so that ABCD is a square and S is the intersection of their diagonals.
- 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. - Four sides of trapezoid
The trapezoid is given by the length of four sides: 40.5 42.5 52.8 35.0. Calculate its area. - Parametric equations
Write the parametric equations of height hc in triangle ABC: A = [5; 6], B = [- 2; 4], C = [6; -1] - Distance of the parallels
Find the distance of the parallels, which equations are: x = 3-4t, y = 2 + t and x = -4t, y = 1 + t (instructions: select a point on one line and find its distance from the other line) - Intersection 3229
Intersection of graphs of functions y = 5x-2 and y = -3x-6
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