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Solution - Distance between two points

The distance between the 2 points is:

d = \sqrt{(400)} = 20

d=sqrt(400)=20

See steps

Step-by-step explanation

1. Plot the two points and calculate the distance using the formula

The coordinates of Point 1 are:
$X_{1} =$ $5$
and $Y_{1} =$ $9$

The coordinates of Point 2 are:
$X_{2} =$ $- 7$
and $Y_{2} =$ $- 7$

d is the distance between the two points.

First, take the square root of both sides of the Pythagorean theorem.

$d^{2} = {(X_{2} - X_{1})}^{2} + {(Y_{2} - Y_{1})}^{2}$

This gives us the distance formula.

$d = \sqrt{({(X_{2} - X_{1})}^{2} + {(Y_{2} - Y_{1})}^{2})}$

Plug the coordinates of the points into the formula

$X_{1} = 5$

$d = \sqrt{({(X_{2} - 5)}^{2} + {(Y_{2} - Y_{1})}^{2})}$

$X_{2} = - 7$

$d = \sqrt{({(- 7 - 5)}^{2} + {(Y_{2} - Y_{1})}^{2})}$

$Y_{1} = 9$

$d = \sqrt{({(- 7 - 5)}^{2} + {(Y_{2} - 9)}^{2})}$

$Y_{2} = - 7$

$d = \sqrt{({(- 7 - 5)}^{2} + {(- 7 - 9)}^{2})}$

Calculate the expression inside the parentheses

$d = \sqrt{({(- 12)}^{2} + {(- 7 - 9)}^{2})}$

$d = \sqrt{({(- 12)}^{2} + {(- 16)}^{2})}$

Simplify numbers raised to exponents

$d = \sqrt{(144 + {(- 16)}^{2})}$

$d = \sqrt{(144 + 256)}$

Simplify the arithmetic

$d = \sqrt{(400)}$

$d = 20$

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Why learn this

Whether it is a quarterback throwing a football, an architect designing a support beam, or a sailor navigating the open seas, many professionals rely heavily on their ability to find the distance between two points.
There is exactly one line between any two points and the distance formula allows us to plug in their coordinates to find the distance between them. This allows us to solve a wide range of real world problems and understand the spatial relationships between objects and spaces around them.

Terms and topics

Distance between two points

Solution - Distance between two points

Step-by-step explanation

1. Plot the two points and calculate the distance using the formula

Why learn this

Terms and topics

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