Finding Equation of Line Using Two Point Form
Equation of line in two point form is found using the steps added below as:
Step 1: First, take any two points that lie on the line. Letβs these points be (x1, y1) and (x2, y2).
Step 2: Use the two-point line formula to find the equation of the line as:
- (y β y1) = (y2 β y1)/(x2 β x1){x β x1}
Step 3: Simplify the equation to get your required equation.
This is explained using the example added below:
Example: Find equation of a line passing through the points (1,2) and (3,4)?
Given points
- A = (1, 2)
- B = (3, 4)
Therefore, x1 = 1, y1 = 2, x2 = 3, y2 = 4
Equation of line in two point form,
- (y β y1) = (y2 β y1)/(x2 β x1){x β x1}
Substitute the values
(y β 4) = (2 β 4)(x-3)/(1 β 3)
(y β 4) = (-2)(x β 3)/(-2)
y β 4 = x β 3
y = x -3 + 4
y = x + 1
Thus, the equation of the line is: y = x + 1
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Two Point Form β Definition, Formula & Derivation
Two-point form of a line is the equation of a line when two points on a line are given, the two-point form formula is Y β y1 = (y2 β y1)/(x2 β x1)(X β x1). Where the two points are, (x1, y1) and (x2, y2). If in geometry two points are given then the equation of the line passing through these two points is given using the two-point form of the line.
In this article, we will learn about the two-point form, the equation of a line in the two-point form, Two Point Form examples, derivation of the two-point form, and others in detail.
Table of Content
- What is Two-Point Form?
- Equation of a Line in Two-Point Form
- Formula For Two Point Form
- Derivation of Two Point Form Formula
- Finding Equation of Line Using Two Point Form
- Two Point Form β Solved Examples
- Practice Questions on Two Point Form