High School Math : How to find the endpoints of a line segment

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #1 : How To Find The Endpoints Of A Line Segment

What is the length of a line with endpoints \(\displaystyle (0,3)\) and \(\displaystyle (5,15)\)?

Possible Answers:

\(\displaystyle 17\)

\(\displaystyle 5\)

\(\displaystyle 12\)

\(\displaystyle \frac{5}{12}\)

\(\displaystyle 13\)

Correct answer:

\(\displaystyle 13\)

Explanation:

The formula for the length of a line is very similiar to the pythagorean theorem:

\(\displaystyle (x_2-x_1)^2+(y_2-y_1)^2=l^2\)

Plug in our given numbers to solve:

\(\displaystyle (x_2-x_1)^2+(y_2-y_1)^2=l^2\)

\(\displaystyle (5-0)^2+(15-3)^2=l^2\)

\(\displaystyle 5^2+12^2=l^2\)

\(\displaystyle 25+144=l^2\)

\(\displaystyle 169=l^2\)

\(\displaystyle \sqrt{169}=\sqrt{l^2}\)

\(\displaystyle 13=l\)

Example Question #2 : How To Find The Endpoints Of A Line Segment

The points A, B, and C reside on a line segment. B is the midpoint of AC. If line AB measures 6 units in length, what is the length of line AC?

Possible Answers:

\(\displaystyle 6\)

\(\displaystyle 12\)

\(\displaystyle 24\)

\(\displaystyle 15\)

\(\displaystyle 18\)

Correct answer:

\(\displaystyle 12\)

Explanation:

If B is the midpoint of AC, then AC is twice as long as AB. We are told that AB=6.

\(\displaystyle A------B------C\)

The diagram shows six units between points A and B, with B as the midpoint of segment AC. Therefore segment BC is also six units long, so line AC is twelve units long.

\(\displaystyle \small (2)(6)=12\)

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