Class 10 Mathematics – Plotting Points, Distance, and Midpoint

1. Plotting Points on a Coordinate Plane

Steps to Plot a Point

1. Start at the origin (0,0).

2. Move horizontally along the X-axis according to the x-coordinate:

   • Positive x → move right

   • Negative x → move left

3. Move vertically along the Y-axis according to the y-coordinate:

   • Positive y → move up

   • Negative y → move down

4. Mark the point.

5. Label the point with its coordinates (x, y).

Tip

• First coordinate (x) → horizontal movement

• Second coordinate (y) → vertical movement

2. Distance Between Two Points (Conceptual)

• Distance is the length of the straight line connecting two points.

• Longer the line → greater the distance.

• Shorter the line → smaller the distance.

• Useful to measure how far apart two points are in a plane.

Practical Examples

• Distance between towns on a map

• Measuring sides of geometric shapes

• Verifying alignment of points

3. Midpoint of a Line Segment (Conceptual)

• Midpoint is the point exactly in the middle of a line segment connecting two points.

• It divides the line segment into two equal parts.

• Useful in geometry for:

  • Finding the center of a line

  • Dividing shapes into equal halves

  • Locating the center of gravity or balance

Practical Examples

• Center of a rectangle or square

• Midpoint between two cities

• Center point for symmetry in designs

4. Quick Tips

• Always label the points clearly.

• Check the quadrant to ensure correct plotting.

• Distance and midpoint help in drawing accurate shapes and solving geometry problems.

• Distance gives size, midpoint gives position.