What is the distance between (2, 3) and (-4, 5)?

Solution:

The distance formula is a variant of the Pythagorean theorem. It is very useful in finding the distance between two points on the XY-plane represented as points (x_1, y₁ ) and (x₂, y₂).

Given: According to the given points, the coordinates are x₁= 2, y₁= 3, x₂= -4, and y₂= 5.

The distance between any two points (x_1, y₁) and (x₂, y₂) is given by,

\(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)

Putting the values of the coordinates in the formula,

⇒ \(d = \sqrt{(-4 - 2)^2 + (5 - 3)^2}\)

⇒ d = √(-6² + 2²)

⇒ d = √(36 + 4)

⇒ d = √40

⇒ d = 2√10

Hence, the distance is 2√10.

Thus, the distance between (2, 3) and (-4, 5) is 2√10.

What is the distance between (2, 3) and (-4, 5)?

Summary:

The distance between (2, 3) and (-4, 5) is 2√10.