# 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, }y_{1} ) and (x_{2}, y_{2}).

Given: According to the given points, the coordinates are x_{1}= 2,_{ }y_{1}= 3,_{ }x_{2}= -4, and y_{2}= 5.

The distance between any two points (x_{1, }y_{1}) and (x_{2}, y_{2}) 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 = √(-6^{2} + 2^{2})

⇒ 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.

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