Chapter 2

Pre Chapter 2:  Video Lesson on Simplifying Radicals       Lesson

Chapter 2.3:  Video Lesson on Distance from a Point to the Origin            Lesson

Chapter 2.4:  Video Lesson on Circles       Lesson

Chapter 2.5:  Video Lesson on Distance Between Two Points        Lesson

Chapter 2.7:  Video Lesson on Midpoints          Lesson

Questions for You to Try

1.  Simplify each of the following radical expressions:

           a)    sqrt(75)                                              Answer:  5 sqrt(3)                           Video Solution

           b)    3 sqrt(3) - sqrt(12)                              Answer:  sqrt(3)                              Video Solution

           c)    [2 sqrt(6) - 5 sqrt(3)] [4 sqrt(2) - 8]      Answer:  56 sqrt(3) - 36 sqrt(6)      Video Solution

           d)    [sqrt(175) - sqrt(28)] / [sqrt(63)]          Answer:  1                                      Video Solution

2.  Determine the distance from P(-7,3) to the origin                   

                                              Answer:  sqrt(58)                     Video Solution

3.  Determine the distance from the point A(-1,6) to B(3,-2)         

                                              Answer:  4 sqrt(5)                   Video Solution

4.  Does the point A(5, -4) lie inside or outside of the circle x^2 + y^2 = 36?  

                                              Answer: Outside                     Video Solution

5.  Determine the midpoint of the line segment from A(-5,-4) to B(3,1)      

                                              Answer:  (-1, -3/2)                   Video Solution

Determining Properties of Triangles

6.    Determine the centroid of the triangle with vertices at A(-4,-2), B(12,6) and C(8,12)    (Quick way and long way)

                                                                                                                       Answer: (16/3, 16/3)         Video Solution

7.    Determine the circumcentre of the triangle with vertices at A(-4,-2), B(12,6) and C(8,12)

                                                                                                                       Answer: (23/8, 17/4)         Video Solution

8.    Determine the orthocentre of the triangle with vertices at A(-4,-2), B(12,6) and C(8,12)

                                                                                                                       Answer: (41/4, 15/2)         Video Solution

9.    Determine the area of the triangle containing vertices A(-1, -3), B(4,9) and C(5,6)

                                                                                                                       Answer:  27/2                    Video Solution

Using Triangle Principles to Determine Lengths

10.    Application of the area of a triangle question:  Determine the shortest distance from the point P(1, -4) to the line       containing the points Q(-4, -2) and R(5, 6)                                                    Answer:  58/[sqrt(145)]      Video Solution