Polygons on the Coordinate Plane
Aligned to 6.G.A.3 — Common Core State Standards for Mathematics.
What this lesson teaches
When a polygon's corners are given as coordinates, you can plot them and find a side's length by subtracting coordinates — horizontal sides use the x-values, vertical sides use the y-values.
Worked examples
Example 1
A rectangle has corners (1, 2), (6, 2), (6, 5), (1, 5). The bottom side length is 6 − 1 = 5, the left side is 5 − 2 = 3, so its perimeter is 2 × (5 + 3) = 16.
Example 2
A triangle has vertices (0, 0), (8, 0), (8, 6). Base 8, height 6, so area = (8 × 6) ÷ 2 = 24 square units.
Example 3
Subtract coordinates to find a side length only when the side is horizontal or vertical. A slanted side needs a different method.
Practice questions
- Plot (2, 1), (2, 6) and find the length of that vertical segment.
- A square has corners (0, 0), (4, 0), (4, 4), (0, 4). Find its perimeter.
- Find the length of the side from (−3, 2) to (5, 2).
Watch the lesson
Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
▶ Watch this lessonEn español
Polígonos en el Plano Cartesiano
Cuando los vértices de un polígono se dan como coordenadas, puedes ubicarlos y hallar la longitud de un lado restando coordenadas: los lados horizontales usan los valores de x, los verticales usan los de y.
Ejemplo 1: Un rectángulo tiene vértices (1, 2), (6, 2), (6, 5), (1, 5). El lado inferior mide 6 − 1 = 5, el lado izquierdo mide 5 − 2 = 3, así que su perímetro es 2 × (5 + 3) = 16.
Ejemplo 2: Un triángulo tiene vértices (0, 0), (8, 0), (8, 6). Base 8, altura 6, así que el área = (8 × 6) ÷ 2 = 24 unidades cuadradas.
Ejemplo 3: Resta coordenadas para hallar el largo de un lado solo cuando el lado es horizontal o vertical. Un lado inclinado necesita otro método.
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