# Precalculus Linear Motion Question?

Florence is 5 meters east and 2 meters north of Paris. Derek is 12 meters west and 9 meters north of Florence. Florence walks in a straight line towards Derek. At the point on her journey where she’s closest to Paris, she turns and walks directly to Paris. How far does Florence walk, in total?

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• Ian H
Lv 7
2 months ago

Do a sketch letting Paris, P, be the origin, and include the line from

Florence F to Derek D and using Pythagoras calculate their distance apart.

Draw in the perpendicular from P meeting FD at T and use similar triangles.

Florence walks FT + TP.

You can do this.

• 2 months ago

My best advice: draw this on a piece of paper with a pencil and ruler. Use the cm ruler markings for the different distances; e.g. a 2cm line for "2m north of Paris".

Make sure to also draw a line connecting Florence and Derek.

To find how far she walks, you have to find the distance she walks before her turn, and the distance after her turn (directly to Paris). Section areas into triangles as needed, and make sure to use the Pythagorean theorem: a^2 + b^2 = c^2.