Skate and Climb: Mirror Positions

Use number lines to identify opposites and reverse a reversal.

Mirror Positions

The skate and climbing gym measures horizontal positions from a center mark at 0. Negative positions are left of center; positive positions are right. A mirror position is a reflection across 0.

A skate practice marker is at +7 meters. Use the number line to find its mirror position.

The mirror position is meters.

Two climbing-route starting holds are at opposite positions. Which pair could be their positions?

A. −6 meters and −6 metersB. −6 meters and +5 metersC. −6 meters and +6 metersD. 0 meters and +6 meters

A climbing hold is 1.5 meters left of the center mark. Its signed position is −1.5 meters. Find its mirror position.

The mirror position is meters.

A route begins at the center mark, 0. What is its position after reflection across 0?

A. Its position is 0.B. Its position is +1.C. Its position is −1.D. Its position cannot be found.

Match each signed route position to its opposite. All positions are in meters.

Membership Reversals

The gym records added membership credit as positive and removed credit as negative. Reversing an adjustment means recording its opposite. Write signed numbers when needed.

Imani's membership record shows a +12 dollar adjustment. Staff reverse that adjustment.

The reversing adjustment is dollars.

Luis's membership record shows a −8.50 dollar adjustment. Which adjustment reverses it?

A. −8.50 dollarsB. +8.50 dollarsC. 0 dollarsD. +0.50 dollars

A membership adjustment is −14 dollars. First find the adjustment that reverses it. Then find the opposite of that reversing adjustment.

The first opposite is dollars. The opposite of that result is dollars.

The expression −(−11) means the opposite of −11. Which number equals −(−11)?

A. −22B. −11C. 0D. 11

10.

A member's adjustment was reversed twice. The final signed adjustment is +6.25 dollars. What was the original signed adjustment?

The original adjustment was dollars.

Check the Route Plans

Use reflections across 0 to check each plan. Each reflection takes the opposite of the current position.

11.

A route planner places a hold at +1 1/4 meters. She reflects its position across 0, then reflects the result across 0 again.

After the first reflection, the position is meters. After the second, it is meters.

12.

A skate marker starts at −9 meters. Eli says reflecting it across 0 twice puts it at +9 meters. Which statement correctly checks his claim?

A. Eli is correct; both reflections leave it at +9 meters.B. Eli is incorrect; the two reflections put it at 0 meters.C. Eli is incorrect; the second reflection returns it to −9 meters.D. Eli is correct; the second reflection keeps it positive.

13.

Two route starts are mirror images across 0 on this scale. One start is at −10 meters. Which description locates the other start?

A. It is five intervals right of 0, at +10 meters.B. It is ten intervals right of 0, at +20 meters.C. It is five intervals left of 0, at −10 meters.D. It is one interval right of 0, at +2 meters.

14.

Sana says, “Reflecting any route position across 0 twice always returns it to its original position, even if it starts at 0.” Explain why she is correct. Use −3.5 meters as an example and also explain the case of 0.