SME
Grade 6 Math · The Number System
The coordinate plane: all four quadrants
Use this for “How far apart are (−4, 3) and (5, 3)?” when two points share a coordinate.
Chart
From (−4, 3) to (5, 3): 9 units.
This is an example. Type your own values to start a new problem.
First point’s x-coordinate
example
First point’s y-coordinate
example
Second point’s x-coordinate
example
Second point’s y-coordinate
example
Distance
calculated
Formulas
Distance from (−4, 3) to (5, 3): 9
Add or subtract the distances from 0 = distance
Assumptions
•
Use two points on the same row (the same y-coordinate) or the same column (the same x-coordinate).
•
On opposite sides of an axis, add the distances from the axis; on the same side, subtract.
•
Coordinates from −10,000 to 10,000; the distance is in units.
Step-by-step
WE KNOW
First point’s x-coordinate: −4
First point’s y-coordinate: 3
Second point’s x-coordinate: 5
Second point’s y-coordinate: 3
FIND
distance
Step 1 · Find distance
Distance from (−4, 3) to (5, 3): ?
Add or subtract the distances from 0 = distance
The points share a coordinate, so count along one line between them.
Same y-coordinate 3: the points are on one row. Use the x-coordinates.
−4 and 5 are on opposite sides of 0: add their distances from 0.
|−4| + |5| = 4 + 5 = 9
Distance = 9
Check
Put the numbers back in. Both sides should match.
|−4| + |5| = 4 + 5 = 9 ✓
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Positive and negative numbers in context
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Reflect points across the axes
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