PSAT Math : Midpoint Formula

Example Questions

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

One endpoint of a line segment on the coordinate plane is . The segment has length 10; the other endpoint has -coordinate 10 and is in Quadrant I. Give the -coordinate of the other endpoint. (Nearest tenth if applicable).

Explanation:

Let  be the -coordinate of the other endpoint.

The segment has endpoints  and .

Apply the distance formula

setting ,

Therefore, there are two values of  which fit the distance criterion.

One is .

However, since the endpoint is in Quadrant I, it must have a positive  coordinate, so this is eliminated as a choice.

The other is , which is correct since it is positive.

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

The midpoint of a line segment is the point . One endpoint is ; give the -coordinate of the other.

Explanation:

Let the endpoints of a line segment be

Then the midpoint of the segment will be

The -coordinate of the midpoint is , and the -coordinate of the known endpoint is , so we can solve for , the -coordinate of the unknown endpoint, in the following equation:

Example Question #3 : How To Find The Endpoints Of A Line Segment

The midpoint of a line segment is the point . One endpoint is ; give the -coordinate of the other.

Explanation:

Let the endpoints of a line segment be

Then the midpoint of the segment will be

The -coordinate of the midpoint is , and the -coordinate of the known endpoint is , so we can solve for , the -coordinate of the unknown endpoint, in the following equation:

Example Question #91 : Coordinate Geometry

The midpoint of a line segment is the point . One endpoint is ; give the -coordinate of the other.

Explanation:

Let the endpoints of a line segment be

Then the midpoint of the segment will be

The -coordinate of the midpoint is , and the -coordinate of the known endpoint is

so we can solve for , the -coordinate of the unknown endpoint, in the following equation:

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

The midpoint of a line segment is the point . One endpoint is ; give the -coordinate of the other.

Explanation:

Let the endpoints of a line segment be

Then the midpoint of the segment will be

The -coordinate of the midpoint is , and the -coordinate of the known endpoint is , so we can solve for , the -coordinate of the unknown endpoint, in the following equation:

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