GMAT Math : Calculating the length of a line with distance formula

Study concepts, example questions & explanations for GMAT Math

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Example Questions

Example Question #1 : Calculating The Length Of A Line With Distance Formula

A line segement on the coordinate plane has endpoints  and . Which of the following expressions is equal to the length of the segment?

Possible Answers:

Correct answer:

Explanation:

Apply the distance formula, setting

:

Example Question #2 : Calculating The Length Of A Line With Distance Formula

What is distance between  and ?

Possible Answers:

Correct answer:

Explanation:

Example Question #3 : Calculating The Length Of A Line With Distance Formula

What is the distance between the points  and ?

Possible Answers:

2\sqrt{5}

Correct answer:

Explanation:

Let's plug our coordinates into the distance formula.

\sqrt{(2-7)^{2}+(5-17)^{2}}= \sqrt{(-5)^{2}+(-12)^{2}} = \sqrt{25+144}= \sqrt{169} = 13

Example Question #4 : Calculating The Length Of A Line With Distance Formula

What is the distance between the points  and ?

Possible Answers:

3\sqrt{3}

2\sqrt{5}

Correct answer:

2\sqrt{5}

Explanation:

We need to use the distance formula to calculate the distance between these two points.

\sqrt{(1-5)^{2}+(4-2)^{2}} = \sqrt{(-4)^{2}+(2)^{2}} =\sqrt{20}=\sqrt{4}\sqrt{5}=2\sqrt{5}

Example Question #5 : Calculating The Length Of A Line With Distance Formula

Consider segment  which passes through the points  and .

Find the length of segment .

Possible Answers:

Correct answer:

Explanation:

This question requires careful application of distance formula, which is really a modified form of Pythagorean theorem.

Plug in everthing and solve:

So our answer is 156.6

Example Question #6 : Calculating The Length Of A Line With Distance Formula

What is the length of a line segment that starts at the point    and ends at the point    ?

Possible Answers:

Correct answer:

Explanation:

Using the distance formula for the length of a line between two points, we can plug in the given values and determine the length of the line segment by calculating the distance between the two points:

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