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Q. 9

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Found in: Page 14

### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465

# If three distinct points P, Q, and R all lie on a line and if $d\left(P,Q\right)=d\left(Q,R\right)$, then Q is called the _________ of the line segment from P to R.

Q is called the midpoint of the line segment from P to R.

See the step by step solution

## Step 1. Given information.

The given statement is:

If three distinct points P, Q, and R all lie on a line and if $d\left(P,Q\right)=d\left(Q,R\right)$, then Q is called the _________ of the line segment from P to R.

## Step 2. Determine the missing term for the blank.

Distance between two-point P and Q is defined as $d\left(P,Q\right)$.

It is given that $d\left(P,Q\right)=d\left(Q,R\right)$, it means, the point Q is equidistant from P and R.

Since P, Q and R lie on a line, therefore Q is the midpoint of the segment PR.

## Step 3. Conclusion.

Q is called the midpoint of the line segment from P to R.