Analytic geometry - math word problems - last page
Number of problems found: 260
- Vector
Determine coordinates of the vector u=CD if C[12;-8], D[6,20].
- XY triangle
Determine the area of a triangle given by line 2x-4y+47=0 and coordinate axes x and y.
- Triangle
Plane coordinates of vertices: K[19, -4] L[9, 13] M[-20, 8] give Triangle KLM. Calculate its area and its interior angles.
- Segment
Calculate the segment AB's length if the coordinates of the end vertices are A[0, -2] and B[-4, 9].
- Circle
The circle touches two parallel lines, p, and q, and its center lies on line a, which is the secant of lines p and q. Write the equation of the circle and determine the coordinates of the center and radius. p: x-10 = 0 q: -x-19 = 0 a: 9x-4y+5 = 0
- Center
Calculate the coordinates of the circle center: x² -4x + y² +10y +25 = 0
- Perpendicular
What is the slope of the perpendicular bisector of line segment AB if A[-1,-4] and B[-6,-7]?
- Cone
If the segment of the line y = -3x +4 that lies in the first quadrant is rotated about the y-axis, a cone is formed. What is the volume of the cone?
- Distance
Calculate the distance between two points K[6; -9] and G[5; -1].
- Circle
Write the equation of a circle that passes through the point [0,6] and touches the X-axis point [5,0]: (x-x_S)²+(y-y_S)²=r²
- Slope
What is the slope of a line with an inclination 3.96 rad?
- Perpendicular
Find the slope of the line perpendicular to the line p: y = 8x +6.
- Line
Line p passes through A[5, -3] and has a direction vector v=(2, 3). Is point B[3, -6] on the line p?
- Center
In the ABC triangle is point D[1,-2,6], which is the center of the |BC|, and point G[8,1,-3], which is the center of gravity of the triangle. Find the coordinates of the vertex A[x,y,z].
- Circle
From the equation of a circle: -x² -y² +16x -4y -59 = 0 Calculate the coordinates of the center of the circle S[x0, y0] and the radius of the circle r.
- Square
Points A[9,9] and B[-4,1] are adjacent vertices of the square ABCD. Calculate the area of the square ABCD.
- Forces
In point, G acts three orthogonal forces: F1 = 16 N, F2 = 7 N, and F3 = 6 N. Determine the resultant of F and the angles between F and forces F1, F2, and F3.
- Angle between lines
Calculate the angle between these two lines: p: -4x +7y +7 =0 q: -x +4y +7=0
- Center
Calculate the coordinates of the center of gravity T [x, y] of triangle ABC; A[-17,9] B[-26,-19] C[-7,7].
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