Question

find the distance between the points p(2
3) and Q(4 1) using distance formula​

Answer 1

Answer:

The distance between the points p(2 ,3) and Q(4,1) = 2√2 units

Step-by-step explanation:

In co-ordinate geometry, The distance between any two points on a line is calculated by the formula

√(x₂ - x₁)² + (y₂ - y₁)²

This is known as the distance formula

Here x1, y1 are coordinates of first point and x2, y2 are coordinates of second point.

We have to find the distance between the points p(2 ,3) and Q(4,1).

Using distance formula,

x₁ = 2, x₂ = 4, y₁ = 3, and y₂ = 1

Distance = √(x₂ - x₁)² + (y₂ - y₁)²

               = √(4 - 2)² + (1 - 3)²

               = √(2)² + (-2)² = √4 + 4 = √8 = 2√2 units

∴ The distance between the points p(2 ,3) and Q(4,1) = 2√2 units

Answer 2

Answer: √8 units

Step-by-step explanation:

Distance Formula for two points P (2,3) and Q (4,1) that form the line PQ is as follows :-

$PQ^{2} = ( x_{2}-x_{1} )^{2} + ( y_{2}-y_{1} )^{2}$

Inputting the values, we get :-

$PQ^{2} = ( 4-2 )^{2} + ( 1-3 )^{2}$

$PQ^{2} = 4 + 4 = 8$

⇒ $PQ = \sqrt{8}$ $units$