Find Axis-Aligned Polygon Sides from Coordinates
Plot the supplied vertices in order and identify the requested side’s shared coordinate.
About 25 minutes, plus any extended practice
Supplied materials
- Paper and a pencil; drawing and spoken explanations are welcome. An adult may read directions and options aloud.
- Supplied worked-case record: A rectangle has vertices (−2,1),(4,1),(4,5),(−2,5).
- All quantities and shape descriptions are supplied in the worked example and questions; no purchase or personal information is needed.
Learn the idea
A polygon can be specified by its ordered vertices on a coordinate plane. Sides joining points with equal x or equal y are axis-aligned, so their lengths are coordinate differences. Across zero, distance includes both signed sides. Connecting vertices in the stated order defines the polygon; rearranging them can change it.
Plot the supplied vertices in order and identify the requested side’s shared coordinate. Subtract endpoint positions to find its nonnegative length. For a rectangle, use recovered horizontal and vertical lengths for area or perimeter when requested.
Plot vertices in the stated connecting order. A coordinate is a signed position; a side length is nonnegative. Draw the signed axes and label each endpoint before measuring the connecting side.
- Draw the signed axes and label each endpoint before measuring the connecting side.
- Work through the supplied example and label what each number or attribute represents.
- Plot the supplied vertices in order and identify the requested side’s shared coordinate.
- Answer the check, then try the three changed-input practice questions and explain one correction.
See the method in action
A rectangle has vertices (−2,1),(4,1),(4,5),(−2,5). Its width is 4−(−2)=6 and height is 5−1=4. Perimeter is twenty units and area twenty-four square units. The negative starting x does not make the side length negative. Plot vertices in the stated connecting order. A coordinate is a signed position; a side length is nonnegative. Draw the signed axes and label each endpoint before measuring the connecting side.
Check your reasoning
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Helpful tips
- Plot vertices in the stated connecting order.
- A coordinate is a signed position; a side length is nonnegative.
See the answer and explanation
6
Find the nonnegative difference in x because y is shared. The result is 6.
Take it further
Rectangle vertices (−3,−1),(2,−1),(2,4),(−3,4) give side lengths 5 and 5, area 25.
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