Coordinate Geometry Class 10 Notes

Coordinate geometry class 10 notes are provided here to help the students of class 10 learn this topic in a more efficient way. This concise notes on Coordinate Geometry Class 10 can also help during revision as students can quickly check the important points and recall the concepts. The points that are covered in these notes are-

  • Coordinate geometry Basics
  • Coordinate Geometry Formulas
    • Distance Formula
    • Section Formula
    • Mid-Point Theorem
  • Area of a triangle
  • Practice Questions

Basics on Coordinate geometry

Coordinate geometry is used to represent a point on a plane. The distance of any given point from y-axis is called its ‘x-coordinate’ or ‘abscissa,’ whereas the distance from the x-axis is called as its ‘y-coordinate’ or ‘ordinate.’ In short, We can easily locate points on a plane with the help of coordinate geometry.

Coordinate geometry helps us to find,

  • Distance between two points
  • Midpoint of a line segment
  • Slope and equation of a line segment
  • If given set of lines are parallel or perpendicular
  • Area and perimeter of a polygon
  • Equations of curves and many more

Coordinate Geometry Class 10 Formulas

Use coordinate geometry formulas to practice questions on this topic. Let’s learn about these formulas in detail with the help of some examples.

  • Distance Formula
  • Section Formula
  • Mid Point Theorem

Distance Formula

Consider a line having two point \(A (x_{1}, y_{1})\) and \(B(x_{2}, y_{2})\), then the distance of these points is given by-

\(AB = \sqrt{(x_{2} – x_{1})^{2} + (y_{2} – y_{1})^{2} }\)

 

The above formula is said to be distance formula.

Coordinate Geometry For Class 10

Section Formula

Section formula is used to divide any line into two parts which are in the ratio m:n.

Let us consider a line AB whose coordinates are given as \(A (x_{1}, y_{1})\) and \(B(x_{2}, y_{2})\),

then the coordinate of the point which divides a line in the given ratio of m:n is given as:

\(\left ( \frac{mx_{2} + nx_{1}}{m + n} , \frac{my_{2} + ny_{1}}{m + n} \right )\)

 

Coordinate Geometry For Class 10
Coordinate Geometry For Class 10

Alternatively, to ease the method of section formula consider the ratio m:n = k,
thus the new ratio becomes ‘k:1′
The section formula is then given as-
\(\left ( \frac{kx_{2} + x_{1}}{k + 1} , \frac{ky_{2} + y_{1}}{k + 1} \right )\)

Mid-Point Theorem

As the name suggests, if a line segment is divided in the ratio 1:1, then the point of division is called as the midpoint of the line segment. The coordinate of the mid-point is given as-

 

\(\left ( \frac{x_{2} + x_{1}}{2} , \frac{y_{2} + y_{1}}{2} \right )\)

 

Area of a Triangle

Consider the triangle formed by the points \((x_{1}, y_{1}), (x_{2}, y_{2}) \;\; and \;\; (x_{3}, y_{3})\), then the area of a triangle is given as-
\(A = \frac{1}{2}\left [x_{1}(y_{2} – y_{3}) + x_{2} (y_{3} – y_{1}) + x_{3} (y_{1} – y_{3}) \right ]\)

Coordinate Geometry For Class 10

Questions on Coordinate Geometry Class 10

  1. In what ratio does the line 2x + y – 4 = 0 divides the line segment joining the
    points A(2, – 2) and B(3, 7).
  2. Calculate the area of the triangle whose vertices are at (2, 3), (–1, 0), (2, – 4).
  3. What would be the value of X if the points A(2, 3), B(4, X) and C(6, –3) are
    collinear.

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