Analytic geometry + line - practice problems - last page
Number of problems found: 135
- Slope
Calculate the slope of a line that intersects points (-6,-25) and (79,23). - Square side
Calculate the length of the side square ABCD with vertex A[0, 0] if diagonal BD lies on line p: -4x -5 =0. - Lie/do not lie
The rule f(x) = 8x+16 gives the function. Find whether point D[-1; 8] lies on this function. Solve graphically or numerically and give reasons for your answer. - XY triangle
Determine the area of a triangle given by line 7x+8y-69=0 and coordinate axes x and y.
- Segment
Calculate the segment AB's length if the coordinates of the end vertices are A[10, -4] and B[5, 5]. - 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 - Perpendicular
What is the slope of the perpendicular bisector of line segment AB if A[9,9] and B[9,-2]? - 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].
- 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]. - Angle between lines
Calculate the angle between these two lines: p: -8x +4y +5 =0 q: 10x +10y -7=0
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