# Analytic geometry - math word problems

Also known as coordinate geometry or Cartesian geometry.

#### Number of problems found: 125

• Ascend vs. descent Which function is growing? a) y = 2-x b) y = 20 c) y = (x + 2). (-5) d) y = x-2
• Distance problem 2 A=(x,2x) B=(2x,1) Distance AB=√2, find value of x
• Distance Calculate distance between two points X[18; 19] and W[20; 3].
• Vector perpendicular Find the vector a = (2, y, z) so that a⊥ b and a ⊥ c where b = (-1, 4, 2) and c = (3, -3, -1)
• Coordinates of vector Determine the coordinate of a vector u=CD if C(19;-7) and D(-16;-5)
• Vector Determine coordinates of the vector u=CD if C[19;-7], D[-16,-5].
• Points collinear Show that the point A(-1,3), B(3,2), C(11,0) are col-linear.
• Intersections 3 Find the intersections of the circles x2 + y2 + 6 x - 10 y + 9 = 0 and x2 + y2 + 18 x + 4 y + 21 = 0
• Coordinates of a centroind Let’s A = [3, 2, 0], B = [1, -2, 4] and C = [1, 1, 1] be 3 points in space. Calculate the coordinates of the centroid of △ABC (the intersection of the medians).
• Three points Three points A (-3;-5) B (9;-10) and C (2;k) . AB=AC What is value of k?
• Distance Wha is the distance between the origin and the point (18; 22)?
• Vector v4 Find the vector v4 perpendicular to vectors v1 = (1, 1, 1, -1), v2 = (1, 1, -1, 1) and v3 = (0, 0, 1, 1)
• Circle - AG Find the coordinates of circle and its diameter if its equation is: ?
• Find the 12 Find the equation of the circle with center (3,7) and circumference 8π units.
• V - slope The slope of the line whose equation is -3x -9 = 0 is
• Center Calculate the coordinates of the circle center: ?
• Distance problem A=(x, x) B=(1,4) Distance AB=√5, find x;
• Center Calculate the coordinates of the center of gravity T [x, y] of triangle ABC; A[11,4] B[13,-7] C[-17,-18].
• Sphere equation Obtain the equation of sphere its centre on the line 3x+2z=0=4x-5y and passes through the points (0,-2,-4) and (2,-1,1).
• Distance between 2 points Find the distance between the points (7, -9), (-1, -9)

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For Basic calculations in analytic geometry is a helpful line slope calculator. From coordinates of two points in the plane it calculate slope, normal and parametric line equation(s), slope, directional angle, direction vector, the length of segment, intersections the coordinate axes etc. See also more information on Wikipedia.