Coordinate Geometry • Topic 3 of 3

Plotting Points in the Plane

How to Plot Points Systematically:

Plotting means marking a point on the Cartesian plane given its coordinates (x, y).

Step-by-Step Plotting Process:

  1. Locate the origin (0, 0)
  2. Move horizontally along the x-axis to the x-coordinate
  3. From that position, move vertically to the y-coordinate
  4. Mark and label the point

Plotting Points with Same x or Same y:

  • Points with same x-coordinate lie on a vertical line
  • Points with same y-coordinate lie on a horizontal line

Plotting Multiple Points:

When plotting several points, it helps to:

  • Plot all points first
  • Label each point clearly
  • Identify patterns (collinear points, shapes)

Connecting Points:

Points can be connected to form geometric shapes:

  • Triangles (3 points)
  • Rectangles and squares (4 points)
  • Other polygons
Section Formula — Point Dividing a SegmentA(x₁,y₁)B(x₂,y₂)P(x,y)mnInternal Division (m:n):x = (mx₂ + nx₁)/(m+n) y = (my₂ + ny₁)/(m+n)Midpoint Formula (m = n = 1):M = ( (x₁+x₂)/2 , (y₁+y₂)/2 )Example: A(2,3), B(8,9) divide in ratio 1:2x = (1×8 + 2×2)/(1+2) = 12/3 = 4 ; y = (1×9 + 2×3)/3 = 5 → P(4,5)
Solved Examples
1
Worked Example

Solve a standard problem on Plotting Points in the Plane.

Solution

Apply the formula/method shown in the concept section above.

Key Points

  • Understand the definition and properties of Plotting Points in the Plane.
  • Study the worked examples and practice similar problems.
  • Always verify your answer using the original conditions.
Quick Check — 4 MCQs
Tap an option to check your answer0 / 4
Q1.To plot $(a,b)$, move $a$ units along the x-axis, then $b$ units:
Explanation: Up/down for $b$.
Q2.Points with the same y-coordinate lie on a line parallel to the:
Explanation: Horizontal line.
Q3.The point $(2,0)$ lies on the:
Explanation: On the x-axis.
Q4.Points of the form $(x,x)$ lie on the line:
Explanation: The line $y=x$.
Practice more MCQs → 📝 Assignment · 35 marks