Coordinate Geometry — Class 10 Mathematics NCERT Solutions (Free)
Free step-by-step NCERT solutions for Class 10 Mathematics chapter "Coordinate Geometry" — 9 important questions with detailed answers for CBSE board exam preparation.
TL;DR: Free step-by-step NCERT solutions for Class 10 Mathematics chapter "Coordinate Geometry" — 9 important questions with detailed answers for CBSE board…
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Key Questions Covered:
- State the distance formula. Find the distance between points A(3, 4) and B(6,…
- Find the coordinates of the point that divides the line segment joining A(2, …
- Prove that the points A(0, 0), B(3, 4), and C(6, 8) are collinear.
- + 6 more questions in the full chapter
Solutions Summary:
| Question | Status |
|---|---|
| State the distance formula. Find the distance between poi… | ✓ Solved |
| Find the coordinates of the point that divides the line s… | ✓ Solved |
| Prove that the points A(0, 0), B(3, 4), and C(6, 8) are c… | ✓ Solved |
Showing 3 of 9 questions
Q1: State the distance formula. Find the distance between points A(3, 4) and B(6, 8).
Distance Formula:
The distance d between two points P(x₁, y₁) and Q(x₂, y₂) in a coordinate plane is:
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
This formula is derived from the Pythagorean theorem.
Problem: Find distance between A(3, 4) and B(6, 8)
Step 1: Identify the coordinates.
Point A: x₁ = 3, y₁ = 4
P...
Q2: Find the coordinates of the point that divides the line segment joining A(2, 3) and B(8, 9) in the ratio 2:1 internally.
Section Formula (Internal Division):
If point P divides the line segment joining A(x₁, y₁) and B(x₂, y₂) internally in the ratio m:n, then:
P = ((m·x₂ + n·x₁)/(m + n), (m·y₂ + n·y₁)/(m + n))
Given:
A(2, 3), B(8, 9)
Ratio = 2:1 (m:n = 2:1)
Step 1: Identify the values.
x₁ = 2, y₁ = 3
x₂ = 8, y₂ = 9
...
Q3: Prove that the points A(0, 0), B(3, 4), and C(6, 8) are collinear.
Given: Points A(0, 0), B(3, 4), C(6, 8)
Prove: These points are collinear (lie on the same line)
Method 1: Using Slope
Step 1: Find the slope of AB.
Slope of AB = (y₂ - y₁)/(x₂ - x₁) = (4 - 0)/(3 - 0) = 4/3
Step 2: Find the slope of BC.
Slope of BC = (8 - 4)/(6 - 3) = 4/3
Step 3: Check if slope...
Showing 3 of 9 questions. Visit the full page for complete solutions.