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Questions and Answers
Match the following steps in constructing a polygon in the Cartesian coordinate plane:
Graph the points = Locate each point's coordinates on the coordinate plane Connect the points = Draw a line between each pair of connected points Check your work = Ensure that the polygon is closed and no points are missed Constructing polygons = Involves graphing points and connecting them with straight lines to form a closed figure
Match the following types of polygons with their descriptions:
Triangle = Polygon with three sides Rectangle = Polygon with four sides and opposite sides are equal and parallel Square = Polygon with four equal sides and four right angles Polygon construction method = Using graphed points and connecting them with lines in the coordinate plane
Match the following vertex coordinates with their corresponding polygon:
(2, 4), (4, 4), (4, 2), (2, 2) = Square (1, 1), (3, 1), (2, 4) = Triangle (0, 0), (6, 0), (6, 4), (0, 4) = Rectangle (3, 3), (7, 3), (7, 7), (3, 7) = Quadrilateral
Match the following actions with their roles in constructing a polygon:
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Study Notes
Constructing polygons in the Cartesian coordinate plane involves graphing points and connecting them with straight lines to form a closed figure. This process can help you find the perimeter and area of the polygon.
To construct a polygon in the coordinate plane, follow these steps:
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Graph the points: Locate each point's coordinates on the coordinate plane. For example, if you have a point at (2, 4), you would plot a point at the intersection of the y-axis at 4 and the x-axis at 2.
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Connect the points: Using a straight edge or a pen, draw a line between each pair of connected points. Make sure to keep the direction of the points' coordinates in mind when connecting them.
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Check your work: Ensure that the polygon you've constructed is closed and that no points are missed. You should be able to trace the polygon without lifting your pen from the paper.
Using this method, you can construct various types of polygons, such as triangles, rectangles, squares, and more. If you have the coordinates of the vertices of the polygon, you can use this method to graph and construct the polygon in the coordinate plane.
For example, if you have a square with vertices at (2, 4), (4, 4), (4, 2), and (2, 2), you would plot each of these points on the coordinate plane and then draw a line between each adjacent pair of points. This would result in a square, as the four points are arranged in a square shape.
In general, constructing polygons in the coordinate plane is a useful skill for understanding the relationships between points and shapes in the coordinate system. It can be applied to various mathematical problems and helps in visualizing complex geometric concepts.
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Description
Learn how to construct polygons in the Cartesian coordinate plane by graphing points and connecting them with straight lines to form closed figures. Understand the process of finding the perimeter and area of polygons through this visualization method.
