IXL | Find the distance between two points

Find the distance between the points

(

–

)

and

(

–

)

Round decimals to the nearest tenth.

units

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Learn with an example

question

Find the distance between the points

(

–

)

and

(

)

Round decimals to the nearest tenth.

units

key idea

The distance between two points can be found using the Pythagorean theorem.

Pythagorean theorem

In a right triangle with leg lengths

and

and hypotenuse length

solution

To find the distance between

(

–

)

and

(

)

you can use the Pythagorean theorem. Draw a right triangle whose hypotenuse connects the two points. The right triangle should have a vertical leg and a horizontal leg to make finding their lengths easier.

Step 1: Calculate the lengths of the right triangle's legs.

You can start with the vertical leg.

The length of the vertical leg is the absolute value of the difference of the

-coordinates:

–

Next, find the length of the horizontal leg.

The length of the horizontal leg is the absolute value of the difference of the

-coordinates:

–

Step 2: Use the Pythagorean theorem to find the length of the hypotenuse.

Plug in the lengths of the legs

144

169

±13

is a distance, so it cannot be negative

The distance between

(

–

)

and

(

)

is 13 units.

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Teacher tools

Work it out

Not feeling ready yet? These can help:

T.1Pythagorean theorem: find the length of the hypotenuse

M.4Distance between two points

O.1Coordinate plane review

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