Chapter

Chapter 2
Section

Practice Test Analytic Geometry

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Solutions
14 Videos

The midpoint of the line segment with endpoints A(-3, -3) and B(1, 5) is at

**A** (-2, 2)

**B** (-4, -8)

**C** (-1, 1)

**D** (1, -1)

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0.27mins

Q1

The length of the line segment with endpoints `C(-5, 2)`

and `D( 1,-4)`

is

**A** `\sqrt{20}`

**B** `\sqrt{24}`

**C** `\sqrt{72}`

**D** `\sqrt{80}`

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0.54mins

Q2

An equation for the circle with centre `(0, 0)`

and radius `4`

is

**A** `x^2 +y^2 = 2`

**B** `x^2 +y^2 = 4`

**C** `x^2 +y^2 = 8`

**D** `x^2 +y^2 = 16`

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0.17mins

Q3

Determine the midpoint coordinates and the length of each line segment.

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1.10mins

Q4

Write an equation for each circle.

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1.06mins

Q5

Rachel makes the following statement: “Since point A is the same distance from both B and C, A is the midpoint of BC.” Is Rachel correct? Explain your reasoning.

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Q6

Jason lives exactly halfway between the primary and secondary schools in his neighbourhood. The intervals between the grid lines represent 1 km.

a) How far apart are the schools?

b) Determine the coordinates of Jason’s home.

c) What other locations are equidistant from the two schools? Explain your reasoning.

d) Determine an equation that represents all locations that are equidistant from the two schools.

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2.33mins

Q7

a) Plot the triangle with vertices A(-2, 1), B(2, -1), and C(0, 5).

b) Determine the lengths of the sides of the triangle.

c) Classify `\triangle ABC`

. Explain your reasoning.

d) Find the area of `\triangle ABC`

.

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4.50mins

Q8

a) Plot the triangle with vertices P(3, 4), Q(-5, 2), and R(1, -4). Then, draw the median from vertex R.

b) Determine an equation for this median.

c) Is this median also an altitude for this triangle? Justify your answer.

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3.08mins

Q9

a) Determine the coordinates of the other endpoint of the diameter shown.

b) does any other point on the circle have an x-coordinate of 3?

c) Determine the equation for the circle.

d) Show that the point you found in part a) can be verified using the equation in part c)

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Q10

a) Determine the coordinates of the midpoints G and H.

b) Verify that GH is parallel to DE.

c) Show that GH is exactly half the length of DE.

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Q11

a) Show that the triangle with vertices. U(4, 3), V(0, -5), and W(-4, -3) is a right triangle.

b) Verify that the median from the right angle to the hypotenuse is half as long as the hypotenuse.

c) Find an equation for the circle that passes through the vertices of `\triangle UVW`

.

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Q12

Scott, Arin, and Dan run a small delivery company. For their business, they use licensed two-way radios with a `20`

-km range. Scott is at their office, which they have marked as the origin on their map of the town. The grid lines on the map are spaced `1`

km apart. Arin is dropping off a package at `(-8, 16)`

while Dan is making a pick-up at `(4, 20)`

.

a) Draw a diagram to represent the reception range for the radio at the office.

b) Find an equation that describes the boundary of this area.

c) Are Arin and Dan both within range of the radio at the office? Justify your answer.

d) Are Arin and Dan Within radio range of each other? Justify your answer.

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2.36mins

Q13

`A(9, 5)`

and `B(5, -9)`

are two points on a circle centered at the origin.

a) Determine an equation for the circle.

b) Determine the midpoint, `C`

, of chord `AB`

.

c) Show that the right bisector of chord `AB`

passes through the center of the circle.

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Q14