# Unit 2: Distances, Circles, Midpoints and Triangles

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

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

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

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

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)

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

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

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