Q&A for How to Use Distance Formula to Find the Length of a Line

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What do we call points that are on same line?

Donagan

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Points on the same straight line are said to be "collinear" or "colinear."

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How do I simplify the square root?

Donagan

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Look for a perfect square inside the radical sign, find its square root, and put that square root out in front of the radical sign, indicating that it's to be multiplied by the radical. For example: √50 = √(2 x 25) = 5√2.

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Question

The rise is 4 inches. The angle is 90 degrees from the height to the base. What is the slope?

Donagan

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To find the slope, you have to know the horizontal distance over which the rise occurs. The 90° angle is not relevant.

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How do I find the distance of a line if I don't know the end points?

Donagan

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Assuming you don't have a measuring tool (tape measure, ruler, etc.), you cannot use the distance formula outlined above without knowing the end points. However, if the line is given as part of a geometrical figure, there are various geometrical and trigonometrical methods to find the length (too numerous and complicated to treat here).

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How would I find the length of each segment?

Community Answer

For a line segment, you should create a right triangle by making two more lines. If this line segment is on a dot grid, every line between two dots is one unit. If the line segment is on a coordinate plane, then you can do the same or use the distance formula for a line.

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A square table has an area of 16 sq cm. How do I find the length of its side?

Donagan

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√16 = 4 cm.

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On a number line, the length of line segment joining 3 and -3 is what?

Donagan

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On a number line 3 and -3 are each 3 units from zero (in opposite directions). So the total distance between them is 3 + 3 = 6.

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Question

Would line AB be the same as line BA?

Donagan

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Yes.

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Question

I don’t understand the distance formula. Can you help?

Donagan

Top Answerer

It's simply the Pythagorean theorem. Find the vertical change (between endpoints of the line). Square it. Find the horizontal change. Square that, too. Add together the two squares. Then find the square root of that sum. This gives you the line length you're looking for.

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If I know the length of the line and one of the endpoints, how do I find the other endpoint?

Donagan

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You can't do it unless you also know the slope of the line.

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Will the radius be half the diameter?

Donagan

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Yes, the radius of any circle is half its diameter.

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