Julie and Doug arrived at Tim's house very excited.
The three friends were going to hear Lisa Byrd sing.
Lisa was a famous performer.
"I can't believe Lisa grew up in our town!" said Julie.
"Her parents own the Byrd Music School where she is performing," said Tim.
"I can't believe our parents are letting us go alone!" said Doug.
"It's not very far," said Tim, rolling his wheelchair to his desk.
"I take piano lessons there every week."
Tim opened a map on his desk.
He followed the streets on the map with his finger.
"You go north on Oak Street, turn east on Elm Drive, then north on Maple Street."
"Here's a shortcut!" said Doug.
He pointed to a path through the park.
"That's not a shorter route," said Tim.
"The streets are straight. The path in the park is squiggly."
"A straight line is the shortest distance between two points," said Julie.
Doug looked at both routes on the map.
"I still think it's shorter to go across the park."
"Hmm," said Julie.
"The shortest distance across an area is a diagonal."
She looked unsure. "Let's measure the length of each route on the map."
Tim picked up a ruler. "I'll measure the streets," he said.
Julie wrote down the lengths of the streets.
Then she added them together.
"The street route is ten centimeters."
"The map scale shows that each centimeter equals two hundred meters," said Tim.
"So it's two kilometers along the streets."
Doug tried to measure the park path.
"It's hard to follow the squiggly line with the ruler."
Tim shook his head. "That won't work."
"I have an idea!" said Julie.
She laid a piece of string over the path.
Then she marked the path's beginning and end on the string.
"Now we can just measure the string!"
Julie stretched the string straight.
Then Doug used the ruler to measure the distance between the two marks.
"It's two kilometers. The same distance as the street route!"
The three kids looked at each other.
"Which way should we go?" asked Tim.
"Through the park!" said Julie. She grinned.
"We can hear the birds sing before we hear Lisa Byrd!"