lesson
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Imagine you are building a rectangular sandbox in a video game, and you have already placed three corner posts at (2,2), (8,2), and (8,7).
A corner point where two sides meet is called a vertex (plural: vertices). Where must the fourth vertex go to complete the rectangle?
📊Interactive diagram
How can we find that missing point without just guessing?
Finding Missing Rectangle Vertices
A rectangle has opposite sides that are straight, equal in length, and meet at 90∘ right angles.
Because the bottom side from (2,2) to (8,2) is horizontal, the top side must also be horizontal at height y=7.
Because the left side must line up vertically with (2,2), its x-coordinate must be 2. Putting those together gives the missing vertex: (2,7).
📊Interactive diagram
What if all four sides must be the exact same length?
Finding Missing Square Vertices
A square is a special rectangle where all four sides have equal length.
If a square has vertices at A(1,1), B(6,1), and C(6,6), the bottom side length is 6−1=5 units.