Coordinate Geometry Class 10 Maths — Revision Notes
This chapter applies algebra to geometry using coordinate axes. Students learn distance formula, section formula, and area calculation using coordinates.
TL;DR: This chapter applies algebra to geometry using coordinate axes. Students learn distance formula, section formula, and area calculation using coordinat…
Written & reviewed by the Syllab.in Academic Team (CBSE/NCERT subject experts) · Updated
This chapter applies algebra to geometry using coordinate axes. Students learn distance formula, section formula, and area calculation using coordinates.
Distance Formula
- Distance between points P(x1, y1) and Q(x2, y2): d = sqrt((x2-x1)^2 + (y2-y1)^2)
- Distance of point (x, y) from origin: d = sqrt(x^2 + y^2)
- Used to find length of line segment
- Can verify if triangle is right-angled using distances
Section Formula
- Point dividing line in ratio m:n has coordinates: ((mx2+nx1)/(m+n), (my2+ny1)/(m+n))
- Midpoint formula: ((x1+x2)/2, (y1+y2)/2) when m = n = 1
- Used to find coordinates of point on line segment
- Internal division when point lies between endpoints
Slope and Angle
- Slope m = (y2 - y1)/(x2 - x1) = tan(θ) where θ is angle with x-axis
- Parallel lines have equal slopes
- Perpendicular lines have slopes m1 and m2 such that m1 x m2 = -1
- Slope is undefined (vertical line) or zero (horizontal line)
Area Using Coordinates
- Area of triangle with vertices (x1,y1), (x2,y2), (x3,y3): |x1(y2-y3) + x2(y3-y1) + x3(y1-y2)|/2
- If area = 0, points are collinear (lie on same line)
- Area of quadrilateral can be found by dividing into two triangles
- Formula extends to polygon with more vertices
Key Terms
- Distance Formula: Formula d = sqrt((x2-x1)^2 + (y2-y1)^2) to find distance between two points
- Slope: Measure of steepness of line = (y2-y1)/(x2-x1)
- Section Formula: Formula to find coordinates of point dividing line segment in given ratio
Frequently Asked Questions
How do you find the area of triangle given coordinates of vertices?
Use formula: Area = |x1(y2-y3) + x2(y3-y1) + x3(y1-y2)|/2 where (x1,y1), (x2,y2), (x3,y3) are vertices.
What does it mean if product of slopes is -1?
If m1 x m2 = -1, then the two lines are perpendicular (meet at right angle).
More Class 10 Maths Revision Notes
- Real Numbers
- Polynomials
- Pair of Linear Equations in Two Variables
- Quadratic Equations
- Arithmetic Progressions
- Triangles
🤖 Stuck on any of these? Ask Syllab's free AI Tutor to explain step by step →