Chapter

Chapter 3
Section

Chapter 1 to 3 Review (pg 156)

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Solutions
20 Videos

Solve the linear system. Explain why you chose the method that you used. Check each solution.

`\begin{array}{lcl} x + 2y = 3 \\ 3x - y = 1\end{array}`

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Q1a

Solve the linear system. Explain why you chose the method that you used. Check each solution.

`\begin{array}{lcl} x - y = -1 \\ 2x + y = 4\end{array}`

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Q1b

Solve the linear system. Explain why you chose the method that you used. Check each solution.

`\begin{array}{lcl} 3x + 2y = 28 \\ 5x - 3y = 15\end{array}`

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Q1c

Solve the linear system. Explain why you chose the method that you used. Check each solution.

`\begin{array}{lcl} \dfrac{1}{2}x + y = 4 \\ x + \dfrac{1}{3}y = 2\end{array}`

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Q1d

All `120`

seats in a hall were filled for a concert. The tickets cost `\$10`

for adults and `\$6`

for students. The total proceeds were `\$980`

.

How many adults attended the concert?

How many students?

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Q2

Two wind turbines generate a total of `57`

kW of power. The larger turbine generates twice as much power as the smaller one. Find the power output of each turbine.

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Q3

A contractor rented a sander for `5`

hour and a polisher for `5`

hour for `\$50`

. For another job, she rented the sander for `4`

h and the polisher for `8`

h.

The rental fees for that job totaled `\$56`

.

Find the hourly rate charged for each tool.

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Q4

Louâ€™s class is selling T-shirts for a fundraiser. The supplier charges `\$750`

for the initial design and set-up plus `\$5`

for each imprinted T-shirt. The students sell the T-shirts for `\$15`

each.

**a)** How many T-shirts do the students need to sell to break even?

**b)** How much profit will the students make if they sell `150`

T-shirts?

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Q5

For his coffee shop, Abdul wants to make a mocha-java blend that will sell for `\$18`

/kg. The mocha coffee beans sell
for `\$20`

/kg, and the java coffee beans sell for `\$15`

/kg. How many kilograms of each kind of coffee bean should he use to make `50`

kg of the mocha-java blend?

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Q6

**a)** Determine the midpoint of each side of `\triangle ABC`

.

**b)** Calculate the perimeter of `\triangle ABC`

.

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Q7

a) Plot the triangle with vertices `D(6, 8), E(1, 8)`

, and `F(4, 2)`

.

b) Determine the equation of the right bisector of side DE.

c) Determine the equation of the right bisector of side EF.

d) Determine the coordinates of the point

of The intersection, M, of the right bisectors in parts a) and b).

e) Show that point M is equidistant from vertices D, E, and F.

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Q8

Classify the triangle with vertices G(-4. -1),H(2, -3), and I(4, 3). Explain your reasoning.

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Q9

M and N are the midpoints of sides JK and KL. Show that MN is parallel to `JL`

.

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Q10

Find an equation for the circle that is centred at the origin and

a) has a radius of 7

b) has a radius of `\sqrt{10}`

c) passes through the point `(-5, 12)`

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Q11

On the plan for a new play area in a park, a paddling pool is represented by a circle with the equation `x^2 + y^2 = 16`

. Dimensions on the plan are in metres. What will the perimeter of the pool be?

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Q12

a) Draw the triangle with vertices `P(-2, -2), Q(2, 4)`

, and `R(8, 0)`

.

b) Show algebraically that `\triangle PQR`

is a right triangle.

c) Is APQR also an isosceles triangle? Use algebraic reasoning to justify your answer.

d) Determine the area of `\triangle PQR`

.

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Q13

a) Plot the triangle with vertices `A(-1, 1), B(3, 5)`

, and `C(5, -1)`

.

b) What type of triangle does `\triangle ABC`

appear to be?

c) Use analytic geometry to verify your answer in part a).

d) Verify that the median from C to AB is also an altitude of the triangle.

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Q15

Use analytic geometry to verify that D[-1, 3), E(2, 2), F[3, -1), and G(0, 0) are the vertices of a parallelogram.

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Q16

JKLM is a trapezoid. P, Q, R, and S are the midpoints of the sides JK, KL, LM, and MJ, respectively. What type of quadrilateral is PQRS? Use analytic geometry to verify your answer.

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Q17

The vertices of rhombus `TUVW`

are `T(-3, 2), U(2, 2), V(0, -2)`

, and `W(5, -2)`

.

Use analytic geometry to show that the diagonals of TUVW are right bisectors of each other.

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Q18