This unit investigates coordinate geometry. Students look at equations for circles and use given information to derive equations for representations of these figures on a coordinate plane. Students also use coordinates to prove simple geometric theorems using the properties of distance, slope, and midpoints. Students will verify whether a figure is a special quadrilateral by showing that sides of figures are parallel or perpendicular.
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Question 1
1.
Identify the center and radius of each circle by dragging it into the correct box on the right.
Center: (2, -1)
Center: (-2, 1)
radius = 5
radius =
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Question 2
2.
A city has a population of 6,688 people. The area of the city is approximately 7.2 square miles. How many people per square mile live in the city? (Round to the nearest tenth.)
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Question 3
3.
Which geometric shape could be used to BEST estimate the total amount of earth the mountain is made of?
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Question 4
4.
Which is an equation for the circle with a center at (–2, 3) and a radius of 3? (Select two.)
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Question 5
5.
Complete the square to convert the circle equation from general to standard form.
1.
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Question 6
6.
What is the center of the circle with the equation:
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Question 7
7.
What is the radius of the circle with the equation:
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Question 8
8.
Which information is needed to show that a quadrilateral is a parallelogram?
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Question 9
9.
Which points are on a circle with a center of (3, –9) and a radius of 5? (Choose 3)
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Question 10
10.
Given the points P(2, –1) and Q(8, 2), what are the coordinates of the point on directed line segment PQ that partitions PQ in the ratio 2:1?
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Question 11
11.
Write the equation of a line that is parallel to y = 3x + 4 through the point (1, 5).
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Question 12
12.
Write the equation of a line that is perpendicular to y = 2x - 7 through the point (2, -3).
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Question 13
13.
Which of the following lines is parallel to y = 3x + 5?
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Question 14
14.
What is the area of the triangle?
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Question 15
15.
What is the equation of this circle?
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Question 16
16.
What is the radius of the circle with the equation:
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Question 17
17.
What is the midpoint of the segment with endpoints (7, 2) and (-1, 8)?
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Question 18
18.
The coordinates of the vertices of a triangle are (3, 3), (9, 3), and (3, 6). Which of the following accurately describes the triangle?
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Question 19
19.
The center of a circle is (4, –2) and its radius is 6. Which point lies OUTSIDE of the circle?
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Question 20
20.
What is the area of a rectangle with vertices at (4, 2), (4, 6), (7, 2) and (7, 6)?
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Question 21
21.
What is the perimeter of a rectangle with vertices at (4, 2), (4, 6), (7, 2) and (7, 6)?
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Question 22
22.
A box is designed so that 4 cans of soup fit tightly into the box, as shown below. Each can has a diameter of 6 centimeters and a height of 10 centimeters. What is the volume of the box?
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Question 23
23.
A city planner laid out a small town on a grid, where each unit on the grid is 5 feet by 5 feet or 25 square feet. The town's park is shown on the grid below.
What is the AREA of the town to the nearest square foot?
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Question 24
24.
A city planner laid out a small town on a grid, where each unit on the grid is 5 feet by 5 feet or 25 square feet. The town's park is shown on the grid below.
What is the PERIMETER of the town to the nearest foot?
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Question 25
25.
A cylindrical tube is designed so three tennis balls, with a diameter of 3 inches each can fit vertically stacked inside of it. What is the volume of this tube to the nearest cubic inch?
