Class 10 / Maths

Class 10 Maths Coordinate Geometry Worksheet

Practice distance formula, midpoint, section formula, triangle area, and collinearity.

advanced45 minutesAnswer key included

Learning objective

Practise distance formula, midpoint, section formula, area of triangle, collinearity, and median length.

Questions

  1. Find the distance between (3, 4) and (7, 1).
  2. Find the distance between (-2, 5) and (4, -3).
  3. Find the midpoint of (6, -2) and (-4, 8).
  4. Find the point that divides (2, 5) and (8, 11) internally in the ratio 1:2.
  5. Find the point that divides (-1, 7) and (5, -5) internally in the ratio 2:1.
  6. Find the area of the triangle with vertices (0, 0), (4, 0), and (0, 3).
  7. Check whether (2, 3), (4, 6), and (6, 9) are collinear.
  8. Find the value of k if (1, 2), (3, k), and (5, 6) are collinear.
  9. Show that (0, 0), (3, 4), and (6, 8) lie on a straight line.
  10. Find the length of the median from A to BC if A(1, 2), B(3, 4), and C(5, 0).

Answer key

Show suggested answers
  1. Distance = sqrt((7 - 3)^2 + (1 - 4)^2) = sqrt(16 + 9) = 5.
  2. Distance = sqrt((4 + 2)^2 + (-3 - 5)^2) = sqrt(36 + 64) = 10.
  3. Midpoint = ((6 + -4)/2, (-2 + 8)/2) = (1, 3).
  4. Using section formula for ratio 1:2, point = ((1 x 8 + 2 x 2)/3, (1 x 11 + 2 x 5)/3) = (4, 7).
  5. Using section formula for ratio 2:1, point = ((2 x 5 + 1 x -1)/3, (2 x -5 + 1 x 7)/3) = (3, -1).
  6. Area = 1/2 x base x height = 1/2 x 4 x 3 = 6 square units.
  7. These points are collinear because the slope between each pair is 3/2, or area of triangle is zero.
  8. For collinearity, slopes must match. (k - 2)/(3 - 1) = (6 - k)/(5 - 3), so k = 4.
  9. (0, 0), (3, 4), and (6, 8) have the same slope 4/3, so they lie on a straight line.
  10. Midpoint of BC = ((3 + 5)/2, (4 + 0)/2) = (4, 2). Median length from A(1, 2) to (4, 2) is 3 units.

How to use this worksheet

Students can solve the questions independently first, then review errors with a parent or teacher. Teachers can use it as a short class activity, homework sheet, or revision check.

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