Geometry
Name_____________________
Assignment #27: Coordinate Geometry I
Due: 2/3/12
Directions: Please show your work for each of the following problems. Be sure to show care in setting up each
scenario, given the following information. Double-check your set-up before attempting to work through each
exercise.
1. Points A, B, C, D have coordinates (1, 5), (6, 8), (8, 6) and (3, 3).
y
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x
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a. Show that AD  BC and AB  DC
b. What type of quadrilateral is ABCD ? Justify your answer.
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Geometry
Name_____________________
Assignment #27: Coordinate Geometry I
Due: 2/3/12
2. A rectangle has vertices at (4, 0), (0, 0), and (0, 3).
y
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x
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a. Find the coordinates of the fourth vertex.
b. Find the length of each diagonal.
c. Algebraically find the coordinates of the intersection point of the diagonals.
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Geometry
Name_____________________
Assignment #27: Coordinate Geometry I
Due: 2/3/12
3. The following are the coordinates of the vertices of EFG: E: (-4, 4), F: (-2, -3), G: (5, 1)
y
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x
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a. Find the lengths of EF and FG .
b. Find the distance from E to G.
c. Find the area of EFG.
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Geometry
Assignment #27: Coordinate Geometry I
Name_____________________
Due: 2/3/12
4. Use a coordinate proof to show that the opposite sides of a parallelogram are congruent.
Geometry
Assignment #27: Coordinate Geometry I
Name_____________________
Due: 2/3/12
5. Use a coordinate proof to show that an isosceles trapezoid has congruent diagonals. Hint:
think of a clever location on the coordinate axes for this isosceles trapezoid, given what you
are trying to prove!
Geometry
Assignment #27: Coordinate Geometry I
Name_____________________
Due: 2/3/12
6. Prove that the diagonals of a rhombus are perpendicular.
Hint: think of a clever location on the coordinate axes for this rhombus, given what you are
trying to prove – be careful not to over-define your rhombus!
Geometry
Assignment #27: Coordinate Geometry I
Name_____________________
Due: 2/3/12
7. Two altitudes are drawn to the legs of an isosceles triangle. Prove that these altitudes have
slopes of opposite signs.