Q. 9 - Precalculus Enhanced with Graphing Utilities

Question

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

Step-by-Step Solution

Answer

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

Step 1. Given information.

The given statement is:

If three distinct points P, Q, and R all lie on a line and if $d(P,Q)=d(Q,R)$, 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 $d(P,Q)$.

It is given that $d(P,Q)=d(Q,R)$, 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.