MathDB

Coordinates Problem

Source:

December 28, 2006

analytic geometrynumber theoryrelatively prime

Problem Statement

Let

Q

. The lines whose equations are

8y=15x

and

10y=3x

contain points

P

and

Q

, respectively, such that

R

is the midpoint of

\overline{PQ}

. The length of

PQ

equals

\frac{m}{n}

, where

m

and

n

are relatively prime positive integers. Find

m+n

.

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