Rina walks in a city park. She walks 30 m east on one path, then 40 m north on another. She has covered 70 m of path in total.
How far from her starting point is she now, in a straight line, and in which direction? The 70 m of walked path answers neither question.
Rina's two walks are displacements: 30 m east, then 40 m north. The straight line from her starting point to her finishing point answers both questions at once. A scale drawing finds that line.
Choose a scale: let 1 cm on paper stand for 10 m on the ground. Draw the first displacement as an arrow 3 cm long, pointing east. Start the second displacement where the first one ends: an arrow 4 cm long, pointing north.
Join the starting point to the finishing point with a straight line. Measure that line with a ruler: 5.0 cm. At 10 m per centimeter, Rina finishes 50 m from her start.
A scale drawing uses 1 cm for every 10 m. A drawn line measures 7.5 cm. Enter the real distance in m.
Jonas draws his two perpendicular walks to scale, the second arrow starting where the first ends. Which drawn line shows his straight-line distance for the whole journey?
Now read the line's direction. The line points between east and north, closer to north than to east. The longer walk tilts the line its way, and here the north walk was the longer one. So the straight-line answer is about 50 m, aimed between east and north.
Alba walks 20 m east, then 60 m north. Her start-to-finish line points between east and north. Which direction is it closer to?
A delivery robot drives 60 m east, then 80 m north. A scale drawing uses 1 cm for every 10 m. The drawn line from start to finish measures 10.0 cm. How far is the robot from its start?
Write down the scale fact:
each centimeter stands for 10 m
Write down the measurement:
the start-to-finish line is 10.0 cm long
Convert the measurement with the scale:
distance = 10.0 × 10 = 100
The robot finishes 100 m from its start, aimed between east and north.
A kayaker paddles 35 m west, then 120 m north. On a drawing at 1 cm per 10 m, the start-to-finish line measures 12.5 cm. How far is the kayaker from the start, and between which directions does the line point?
Write down the scale fact:
each centimeter stands for 10 m
Write down the measurement:
the start-to-finish line is 12.5 cm long
Convert the measurement with the scale:
distance = 12.5 × 10 = 125
The kayaker finishes 125 m from the start. The line points between west and north, closer to north, because the north leg was the longer one.
A hiker walks 90 m east, then 120 m north. On a scale drawing at 1 cm for every 25 m, the line from start to finish measures 6.0 cm. Enter the hiker's straight-line distance from the start in m.
A drone flies 80 m north, then 20 m east. Which statement about the drone's straight-line distance from its start is correct?
A kayaker paddles 70 m north, then 70 m east. Between which directions does the start-to-finish line point?