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Phone Plans: How Close Is the Match?

Use coordinate distances to compare phone and data plan profiles.

Answer Key

Read the Comparison Chart

A comparison tool gives each phone plan a data-value score (x) and a coverage score (y), both measured relative to a benchmark. Negative scores are below the benchmark. Distances are in chart units, not dollars or gigabytes. Use straight-line distance throughout.

−5−4−3−2−1123450−5−4−3−2−112345ABCDData-value scoreCoverage score
Use the four plan profiles on this chart for Questions 1–4.
1.
What is the exact distance between profiles A and B?
  • A. √45 chart units
  • B. √27 chart units
  • C. 9 chart units
  • D. 45 chart units
2.

How far apart are profiles A and C? 5 chart units

3.
A student currently uses plan B. Which other profile is closest to B on the chart?
  • A. Profile A is closest.
  • B. Profile C is closest.
  • C. All three are equally close.
  • D. Profile D is closest.
4.
Which calculation correctly finds the distance between profiles C and D?
  • A. 5 + 6 = 11 chart units
  • B. √(3² + 0²) = 3 chart units
  • C. √(6² − 5²) = √11 chart units
  • D. √(5² + 6²) = √61 chart units

Make a Plan Decision

Each question uses a new comparison. Continue to treat both coordinates as scores in chart units. Use exact distances unless rounding is requested.

5.
Mina's target profile is (1, −1). She will consider only plans at most 5 chart units from her target. Which eligible plan has the lowest monthly price?
Plans Under Review
PlanProfileMonthly price
Cedar(−3, 2)$24
Harbor(4, 3)$21
Summit(1, 5)$18
Vale(−5, −1)$19
  • A. Harbor is the lowest-priced eligible plan.
  • B. Cedar is the lowest-priced eligible plan.
  • C. Vale is the lowest-priced eligible plan.
  • D. Summit is the lowest-priced eligible plan.
6.
A plan update changes its profile from (0.5, −1.5) to (3, 4.5). Find the exact distance between the old and new profiles.

Distance: 6.5 chart units

7.
A comparison alert appears when two profiles are more than 9 chart units apart. Profiles J and K are at (−4, 1) and (3, −5). Which statement correctly decides whether the alert appears?
  • A. No alert appears because 7 is less than 9.
  • B. No alert appears because √85 rounds to 9.
  • C. An alert appears because √85 is greater than 9.
  • D. An alert appears because 13 is greater than 9.
8.
A saved plan profile is (−2, −3). A second profile is (n, 9), lies to the left of the saved profile, and is exactly 15 chart units away.

What is the missing x-coordinate, n? -11

9.
Dev's target is the benchmark, (0, 0). Which list orders these profiles from closest to farthest from his target?
Dev's Shortlist
PlanProfile
Birch(−2, −2)
Cove(1, 3)
Mesa(−3, 2)
Pine(0, −4)
  • A. Pine, Mesa, Cove, Birch
  • B. Birch, Cove, Mesa, Pine
  • C. Cove, Birch, Mesa, Pine
  • D. Birch, Cove, Pine, Mesa

Check the Comparison Tool

Check the graph scale and distinguish exact distances from rounded values. Explain your reasoning in the final question.

10.
Two plans have profiles (−4.5, 2) and (2.5, 2). Their coverage scores are equal.

What is the distance between their profiles? 7 chart units

11.
The tool groups pairs of profiles that have equal separation. Which pair is the same distance apart as (−3, −1) and (1, 6)?
  • A. The pair (0, 0) and (7, 7).
  • B. The pair (0, 0) and (4, 6).
  • C. The pair (0, 0) and (4, 7).
  • D. The pair (−1, 0) and (6, 3).
12.
This chart labels every 2 score units. Find the distance between profiles L and M.−8−6−4−224680−8−6−4−22468LMData-value scoreCoverage score

Distance: 10 chart units

13.
A comparison report connects profiles at (−3, 4) and (5, −2). A second report connects profiles at (−2, 2) and (3, −1). How much longer is the first connection? Round only your final answer to the nearest tenth.

The first connection is 4.2 chart units longer.

14.
Ravi's target profile is T. The app rounds each distance to the nearest whole chart unit and displays 5 for both N and P. Ravi says, “These plans are equally close to my target.” Use exact distances to evaluate his claim and identify the closer profile.−5−4−3−2−1123450−5−4−3−2−112345TNPData-value scoreCoverage score

Ravi's claim is incorrect. TN = √(4² + 3²) = 5 chart units. TP = √(5² + 1²) = √26 chart units. Since 26 > 25, √26 > 5, so N is closer to T. Both distances round to 5, but equal rounded values do not mean the exact distances are equal.