Textbook

10 Principles of Mathematics Nelson
Chapter

Chapter 2
Section

Analytic Geometry Chapter Review

Purchase this Material for $8

You need to sign up or log in to purchase.

Subscribe for All Access
You need to sign up or log in to purchase.

Solutions
25 Videos

On the design plan for a garden, a straight path runs from `(-25, 20)`

to `(40, 36)`

. A lamp is going to be placed at the midpoint of the path. Determine the coordinates for the lamp.

Buy to View

Plus Content!
0.00mins

Q1

`\triangle ABC`

has vertices at `A(-4, 4), B(-4, -2)`

, and `C(2, -2)`

.

a. Determine the equation of the median from `B`

to `AC`

.

b. Is the median for part a) also an altitude? Explain how you know.

Buy to View

Plus Content!
2.02mins

Q2

`\triangle LMN`

has vertices at `L(O, 4), M(-5, 2)`

, and `N(2, -2)`

. Determine the equation of the perpendicular bisector that passes through `MN`

.

Buy to View

Plus Content!
1.59mins

Q3

Which point is closer to the origin: `P(-24, 56)`

or `Q(35, -43)`

?

Buy to View

Plus Content!
1.01mins

Q4

A builder needs to connect a partially built house to a temporary power supply. On the plan, the coordinates of the house are `(20, 110)`

and the coordinates of the power supply are `(105, 82)`

. What is the least amount of cable needed?

Buy to View

Plus Content!
0.56mins

Q5

`\triangle QRS`

has vertices at Q(2, 6), R(—3, 1), and 5(6, 2). Determine the perimeter of the triangle.

Buy to View

Plus Content!
2.13mins

Q6

`\triangle XYZ`

as vertices at `X(1, 6)`

, `Y(-3, 2)`

, and `Z(9, 4)`

. Determine the length of the longest median in the triangle.

Buy to View

Plus Content!
2.33mins

Q7

a. Determine the equation of the circle that is centred at `(0, 0)`

and passes through point
`(-8, 15)`

.

b. Identify the coordinates of the intercepts and three other points on the circle.

Buy to View

Plus Content!
1.31mins

Q8

A circle has a diameter with endpoints `C(20, -21)`

and `D(-20, 21)`

. Determine the equation of the circle.

Buy to View

Plus Content!
1.51mins

Q9

Determine the equation of this circle.

Buy to View

Plus Content!
0.16mins

Q10

The point `(-2, k)`

lies on the circle `x^2 + y^2 = 20`

. Determine the values of `k`

. Show all the steps in your solution.

Buy to View

Plus Content!
0.50mins

Q11

`\triangle ABC`

has vertices as shown. Use analytic geometry to categorize `\triangle ABC`

. Show your work.

Buy to View

Plus Content!
1.03mins

Q12

A triangle has vertices at `A(1, 1), B(-2, -1)`

, and `C(3, -2)`

. Calculate the side lengths to determine whether the triangle is isosceles, equilateral, or scalene.

Buy to View

Plus Content!
1.12mins

Q13

Show that the quadrilateral with vertices at `J(-1, 1), K6, 4), L(8, 4)`

, and `M(4, 1)`

is a rhombus. What is the length of the side?

Buy to View

Plus Content!
2.13mins

Q14

Determine the type of quadrilateral described by the vertices `R(-3, 2), 5(- 1, 6), T(3, 5)`

, and `U(1, 1)`

. Show all the steps in your solution.

Buy to View

Plus Content!
2.52mins

Q15

A quadrilateral has vertices at `A(-3, 1), B(-5, -9), C(7, -1)`

, and `D(3, 3)`

. The mid segments of the quadrilateral form ?

Buy to View

Plus Content!
2.07mins

Q16

Which of the points `A(10, 10),B (-7, 3)`

, and `C(0, -14)`

lie on a circle with centre `O(5, -2)`

? What is the radius of this circle?

Buy to View

Plus Content!
2.26mins

Q17

A triangle has vertices at `P(-2, 7), Q(-4, 2)`

, and `R(6, -2)`

.

a. Categorize `\triangle PQR`

.

b. Show that the mid point of the hypotenuse is the same distance from each vertex. What is the distance?

Buy to View

Plus Content!
3.38mins

Q18

Show that points (6, 7) and (-9, 2) are the endpoints of a chord in a circle with centre (0, 0).

Buy to View

Plus Content!
3.03mins

Q19

Quadrilateral `JKZM`

has vertices as shown. Show that the diagonals of the quadrilateral bisect each other by showing they share the midpoint. What is the mid point?

Buy to View

Plus Content!
1.35mins

Q20a

`\triangle PQR`

has vertices at `P(0, -2), Q(4, 4)`

, and `R(-4, 5)`

. Use analytic geometry to determine
the coordinates of the orthocentre (the point where the altitudes intersect).

Buy to View

Plus Content!
5.56mins

Q21

`\triangle XYZ`

has vertices at `X(0, 1), Y(6, -1)`

, and `Z(3, 6)`

. Use analytic geometry to determine the coordinates of the centroid (the point where the medians intersect).

Buy to View

Plus Content!
1.41mins

Q22

A new lookout tower is going to be built so that it is the same distance from three ranger stations. If the stations are at `A(-90, 28), B(0, -35)`

, and `C(125, 20)`

on a grid, determine the coordinates of the point where the new tower should be built.

Buy to View

Plus Content!
5.47mins

Q23

Predict the type of quadrilateral that is formed by the points of intersection of the lines `3x+y-4=0`

, `4x-5y+30=0`

,
`4y = -3x -1`

, and `-4x + 5y +10 = 0`

. Give reasons for your prediction. Verify that your prediction is correct by solving this problem.

Buy to View

Plus Content!
2.11mins

Q24

A builder wants to run a temporary line from the main power line to a point near his site office. On the site plan, the site office is at `S(25, 18)`

and the main power line goes through points `T(1, 5)`

and `U(29, 12)`

. Each unit represents 1 m.

a. At what point should the builder connect to the main power line?

b. What length of cable will the builder need?

Buy to View

Plus Content!
3.17mins

Q25