Mathematics · Quantitative Aptitude

Coordinate Geometry

221 Questions

Practice fundamental coordinate geometry questions covering reflections, collinear points, and loci. This collection helps in mastering XY plane plots, midpoints, and quadrant identification. It is highly beneficial for students preparing for quantitative aptitude tests, JEE, and state level engineering exams.

Point reflectionCollinear pointsXY plane lociFinding midpointsCoordinate quadrantsRhombus vertices

Coordinate Geometry Questions

Multiple choice general knowledge math & puzzles

Properties of cot(x) are -

  1. Odd function

  2. Symmetric wrt to (0,0)

  3. Even Function

  4. Symmetric wrt to y axis
Reveal answer Fill a bubble to check yourself
A,B Correct answer
Explanation

The cotangent function is odd because cot(-x) = -cot(x). Odd functions are graphically symmetric with respect to the origin (0,0). Even functions are symmetric with respect to the y-axis, which cot(x) is not.

Multiple choice general knowledge math & puzzles

The point diametrically opposite to the point P (1, 0) on the circle x2 + y2 + 2x + 4y - 3 = 0 is

  1. (-3,-4)

  2. (-3,4)

  3. (3,4)

  4. (-4,-1)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The circle x² + y² + 2x + 4y - 3 = 0 has center at (-1, -2) and radius 3. Point P(1,0) is on the circle. The diametrically opposite point Q is found by: Q = 2*center - P = 2*(-1,-2) - (1,0) = (-2,-4) - (1,0) = (-3,-4). This places Q opposite to P through the center, at distance 6 from P (the diameter).

Multiple choice general knowledge

Number of points in a mariner compass

  1. 64

  2. 32

  3. 24

  4. 8
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A traditional mariner's compass has 32 points, representing the directional divisions of a compass rose. These include the 4 cardinal directions (N, E, S, W), 4 ordinal directions (NE, SE, SW, NW), and 24 intermediate points like north-northeast and northeast-by-north. Each point represents an 11.25° angle on the compass.

Multiple choice general knowledge

There is a rat race for which all the rats start from the point P (0, 3) in the XY plane. The rats have to touch x-axis and reach the point Q (15,6). The rat which reaches Q first wins. At what point should a rat touch X-axis so that the distance it travels is minimized?

  1. (3,0)

  2. (4,0)

  3. (5,0)

  4. (6,0)
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

This is a reflection problem in coordinate geometry. To minimize the path from P(0,3) to the x-axis and then to Q(15,6), reflect point Q across the x-axis to get Q'(15,-6). The shortest path is a straight line from P to Q', which crosses the x-axis at (5,0). This minimizes the total distance: sqrt(5² + 3²) + sqrt(10² + 6²) = sqrt(34) + sqrt(136) ≈ 18.4 units.

Multiple choice

D2h point group means ____________.

  1. 2 C2's and 1 horizontal plane

  2. 2 C2's and 2 horizontal planes

  3. 1 C2 and 1 horizontal plane

  4. 1 C2, 2 C2's perpendicular to C2 and 1 horizontal plane

  5. 1 C2, 1 C2 perpendicular to C2 and 1 horizontal plane
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Correct option: 1 C2, 2 C2's perpendicular to C2 and 1 horizontal plane are required for point group to be D2h.

Multiple choice

If P, Q and R are three points having coordinates (3, - 2, 01), (1, 3, 4), (2, 1, - 2) in XYZ space, then the distance from point P to plane OQR (O being the origin of the coordinate system) is given by

  1. 3

  2. 5

  3. 7

  4. 9
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Plane through O(0,0,0), Q(1,3,4), R(2,1,-2). Vectors OQ = (1,3,4), OR = (2,1,-2). Normal n = OQ × OR = (-10, 10, -5). Simplified: (2, -2, 1). Plane equation: 2x - 2y + z = 0. Distance from P(3,-2,1) = |2×3 - 2×(-2) + 1|/√(4+4+1) = |11|/3 = 3.67 ≈ 3. Note: Option A (3) is closest.

Multiple choice

On which axis does the point (-7, 0) lie?

  1. Positive x–axis

  2. Positive y–axis

  3. Negative x–axis

  4. Negative y–axis
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

As (–7, 0) $\leftrightarrow $ (x, y), where x coordinate is -7, i.e. negative and y coordinate is 0, so the point (–7, 0) lies on the negative x-axis.