Coordinate Geometry: Following Cardinal Directions

Which dot is located farthest north (highest y-value) on the coordinate plane?

• Olive dot at (0, 6)

• Blue dot at (3, 6)

• Gray dot at (4, 8)

• Orange dot at (8, 4)

Which dot is located farthest east (highest x-value) on the coordinate plane?

• Green dot at (6, 3)

• Red #2 dot at (6, 0)

• Gray dot at (4, 8)

• Orange dot at (8, 4)

The red dot at (0, 0) is located directly south of which dot? (directly south means same x-coordinate, lower y-value)

• Magenta dot at (1, 2)

• Olive dot at (0, 6)

• Cyan dot at (2, 1)

• Blue dot at (3, 6)

Starting at the blue dot (3, 6), you travel 3 units east and then 3 units south. Which dot do you land on?

• Orange dot at (8, 4)

• Green dot at (6, 3)

• Red #2 dot at (6, 0)

• Gray dot at (4, 8)

Which pair of dots are aligned directly north and south of each other (share the exact same x-coordinate)?

• Blue (3, 6) and Gray (4, 8)

• Magenta (1, 2) and Cyan (2, 1)

• Green (6, 3) and Red #2 (6, 0)

• Olive (0, 6) and Blue (3, 6)

Starting at the orange dot (8, 4), you travel 2 units west and 1 unit south. Which dot is your new location?

• Green dot at (6, 3)

• Gray dot at (4, 8)

• Red #2 dot at (6, 0)

• Blue dot at (3, 6)

A student claims the red dot at (6, 0) doesn’t belong because it is the only dot on the x-axis. Which response best evaluates this claim?

• The claim is incorrect — the red dot at (0, 0) also lies on the x-axis, so two dots share this property.

• The claim is incorrect — every dot touches an axis somewhere.

• The claim is correct because (0, 0) lies on the y-axis, not the x-axis.

• Gray dot at (4, 8) — because 8 is double 4

• Blue dot at (3, 6) — because 6 is double 3

• Olive dot at (0, 6) — because y=6 and 2x=0

• Magenta dot at (1, 2) — because 2 equals 2(1)

You travel from the olive dot (0, 6) east to the gray dot (4, 8) (east then north), and then continue east toward the orange dot (8, 4). Which dot do you pass directly through on the first leg of this journey?

• Blue dot at (3, 6) — same y-value as olive, crossed while traveling east

• Green dot at (6, 3) — passed while traveling east from gray

• Magenta dot at (1, 2) — landed on during some step

• Cyan dot at (2, 1) — passed while traveling south

Using cardinal direction reasoning, which dot is the strongest case for “doesn’t belong” because it is the only dot that cannot be reached from any other dot by traveling in a single cardinal direction?

• Orange dot (8, 4) — it is the farthest dot from the origin