Signed numbers and coordinates
Try these fresh problems without your notes. Explain your method before opening a solution. This practice is not a graded school assessment.
Check 1
Which statement is true?
Check 2
Reflect (−4, −2) across the x-axis.
Challenge 1
A lift moves from floor −3 to floor 7 and back to floor 2. Find the total distance in floor intervals and the overall signed change.
Show a hint
Add the lengths of both legs for distance; compare final with initial for change.
Show the worked solution
Distance 15 floor intervals; signed change +5.
The legs are |7 − (−3)| = 10 and |2 − 7| = 5, totalling 15. Overall change is 2 − (−3) = +5.
Challenge 2
A rectangular path joins (−2, −3), (3, −3), (3, 1), (−2, 1), then returns to the start. Find its length.
Show a hint
Find a horizontal and a vertical side, then use both pairs.
Show the worked solution
18 units.
Horizontal sides measure 5 units and vertical sides 4. Total length is 2 × 5 + 2 × 4 = 18.
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