Coordinate Geometry — Questions & Answers

Sample questions from Coordinate Geometry

1. Q1. In what ratio is the join of (2, −3) and (5, 6) cut by the x-axis?

   • A.1 to 2✓
   • B.2 to 1
   • C.1 to 1
   • D.3 to 1
   Solution

   A is correct. On the x-axis y = 0, so with the ratio taken as k to 1 the section formula gives (6k − 3)/(k + 1) = 0, so 6k = 3 and k = 1/2, that is the ratio 1 to 2. B inverts it, which would put the dividing point nearer the second endpoint when in fact it is nearer the first. C would need the two y coordinates to be equal in size and opposite in sign, and −3 and 6 are not. D comes from solving 6k = 3 as k = 3, dividing the wrong way round.

2. Q2. Why does a triangle area become zero for collinear vertices? Apply the same coordinate reasoning to another figure:

   • A.The three points lie on one line and enclose no region✓
   • B.The sides become equal
   • C.The coordinates disappear
   • D.The triangle becomes equilateral
   Solution

   Collinear points do not enclose a two-dimensional area.

3. Q3. Reflection of (x,y) in the x-axis is:

   • A.(x,−y)✓
   • B.(−x,y)
   • C.(−x,−y)
   • D.(y,x)
   Solution

   Reflection in x-axis changes the sign of y.

4. Q4. Why are opposite vertices of a parallelogram related by the same midpoint? Apply the same coordinate reasoning to another figure:

   • A.Diagonals bisect each other✓
   • B.All sides are equal
   • C.Angles are all right
   • D.It has no diagonals
   Solution

   The diagonals of a parallelogram share the same midpoint.

5. Q5. The distance between (0, 0) and (a, 0) is:

   • A.a, always
   • B.The size of a✓
   • C.a²
   • D.0
   Solution

   B is correct: the distance is the square root of a², which is the size of a and never negative. A is wrong when a is negative, and that is the whole point of the distinction. C forgets the square root. D would need the two points to coincide.

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