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Additional Example 1A: Using Coordinates to Classify Quadrilaterals

In computer graphics, a coordinate system is used to create images, from simple geometric figures to realistic figures used in movies. Properties of the coordinate plane can be used to find information about figures in the plane, such as whether lines in the plane are parallel.

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Additional Example 1A: Using Coordinates to Classify Quadrilaterals

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  1. In computer graphics, a coordinate system is used to create images, from simple geometric figures to realistic figures used in movies. Properties of the coordinate plane can be used to find information about figures in the plane, such as whether lines in the plane are parallel.

  2. Additional Example 1A: Using Coordinates to Classify Quadrilaterals Graph the polygons with the given vertices. Give the most specific name for the polygon. A(0, –2), B(3, 3), C(3, –2) Step 1: Classify the polygon by its angles. C is a right angle, so triangle ACB is a right triangle.

  3. Additional Example 1A Continued Step 2: Classify the triangle by its sides. Find the length of each side. AC = |3 – 0| = 3 BC = |–2 – 3| = 5 The triangle has no congruent sides, so it is scalene. Triangle ACB is a right scalene triangle.

  4. Additional Example 1B: Using Coordinates to Classify Quadrilaterals Graph the polygons with the given vertices. Give the most specific name for the polygon. L(2, 1), M(5, 1), N(5, –1), P(2, –1) Examine the sides of the quadrilateral. LM and PN are parallel. LP and MN are parallel. The quadrilateral is a rectangle because it has two sets of parallel sides and the sets of parallel sides are different lengths.

  5. Check It Out: Example 1 Graph the polygons with the given vertices. Give the most specific name for the polygon. Q(–2, 3), R(1, 5), S(1, –2), T(–2, –4) Examine the sides of the quadrilateral. QT and RS are parallel. The quadrilateral is a parallelogram because it has two sets of parallel sides and the sets of parallel sides do not form 90 angles. QR and TS are parallel.

  6. Additional Example 2A: Finding the Coordinates of a Missing Vertex Find the coordinates of each missing vertex. Triangle ABC has a right angle at C and AC = 2. Find one set of possible coordinates for A. Since BC is horizontal, AC must be vertical for the triangle to have a right angle at C. (4, 0) or (4, –4)

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