Coordinate Geometry

What you'll learn

Learn the distance formula, section formula, and midpoint formula to solve Class 10 Coordinate Geometry problems on the x-y plane with confidence.

This chapter has

Coordinate Geometry — solved practice questions

8 Class 10 Mathematics questions with step-by-step solutions. Attempt each, then reveal the answer.

1. Q1medium

   The distance between two points (x₁,y₁) and (x₂,y₂) is:

   • A√[(x₂−x₁)²+(y₂−y₁)²]
   • B(x₂−x₁)+(y₂−y₁)
   • C√[(x₂+x₁)²+(y₂+y₁)²]
   • D|x₂−x₁|+|y₂−y₁|
   Show answer & solution

   Correct answer: (A) √[(x₂−x₁)²+(y₂−y₁)²]

   Distance = √[(x₂−x₁)² + (y₂−y₁)²].

2. Q2easy

   The distance of the point (3, 4) from the origin is:

   • A3
   • B4
   • C5
   • D7
   Show answer & solution

   Correct answer: (C) 5

   Distance = √(3²+4²) = √(9+16) = √25 = 5.

3. Q3easy

   The midpoint of the line segment joining (2, 4) and (6, 8) is:

   • A(3, 5)
   • B(4, 6)
   • C(8, 12)
   • D(2, 4)
   Show answer & solution

   Correct answer: (B) (4, 6)

   Midpoint = ((2+6)/2, (4+8)/2) = (4, 6).

4. Q4medium

   The midpoint formula for a segment joining (x₁,y₁) and (x₂,y₂) is:

   • A((x₁+x₂)/2, (y₁+y₂)/2)
   • B(x₁+x₂, y₁+y₂)
   • C((x₁−x₂)/2, (y₁−y₂)/2)
   • D(x₁x₂, y₁y₂)
   Show answer & solution

   Correct answer: (A) ((x₁+x₂)/2, (y₁+y₂)/2)

   Midpoint = ((x₁+x₂)/2, (y₁+y₂)/2).

5. Q5hard

   The section formula divides the join of (x₁,y₁) and (x₂,y₂) in ratio m:n internally as:

   • A((mx₁+nx₂)/(m+n), …)
   • B((mx₂+nx₁)/(m+n), …)
   • C((mx₂−nx₁)/(m−n), …)
   • Dnone of these
   Show answer & solution

   Correct answer: (B) ((mx₂+nx₁)/(m+n), …)

   Point = ((mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n)).

6. Q6easy

   The point that divides (1,2) and (5,6) in ratio 1:1 is:

   • A(2, 3)
   • B(4, 5)
   • C(3, 4)
   • D(6, 8)
   Show answer & solution

   Correct answer: (C) (3, 4)

   1:1 division is the midpoint = ((1+5)/2, (2+6)/2) = (3, 4).

7. Q7medium

   What is the distance between (0, 0) and (5, 12)?

   • A11
   • B12
   • C13
   • D17
   Show answer & solution

   Correct answer: (C) 13

   √(25+144) = √169 = 13.

8. Q8medium

   The area of a triangle with vertices (0,0), (a,0) and (0,b) is:

   • Aab
   • Bab/2
   • C2ab
   • Da+b
   Show answer & solution

   Correct answer: (B) ab/2

   Area = ½ |x₁(y₂−y₃)+x₂(y₃−y₁)+x₃(y₁−y₂)| = ½|a×b| = ab/2.

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