Tag: analytic geometry

MPM2D Unit 2 Assessment Schedule 2016-10-19

Here’s what’s happening for my classes in the next few days:

Date MPM2D1-01 MPM2D1-02
Thursday 20th OSSLT all morning No math class (OSSLT)
Friday 21st No math class Double math: period 1 review, period 2 open-book assignment
Monday 24th Period 1 open-book assignment Period 2 closed-book test
Tuesday 25th Period 1 closed-book test Period 2 start of next unit

MPM2D Wrapping up Analytic Geometry 2016-10-13

We finished our work on Equations of Circles today. I’ll post a “completed” version of that handout when I have time to put it together.

Here’s a review task for this unit. It’s 18 questions long, and it takes a while. For example, finding the equation of the line that gives the shortest distance from a point to another line (question 8) has a lot of steps. Spend at least 15 minutes on the review tonight; we’re going to be continuing to work on it tomorrow in class. You can get help from your friends on this!

Anayltic Geometry Giant Review

I’m planning to have an in-class assignment and a test next week. My current plan is to have the assignment on Wednesday, October 19th and the test on Friday, October 21st. Stay tuned in case we need to change that slightly – I might have some more activities for you to work on before those assessments.

MPM2D1-02 Circumcentre and Centroid 2016-10-06

We used cardboard triangles today. We drew the three medians on one side and the three perpendicular bisectors to the sides on the other. 

We noticed that the perpendicular bisectors all met in a single point, and that a circle centred on that point could be drawn so that each vertex of the triangle would be on the circumference. This point is called the circumcentre.

We also noticed that the medians connected in a single point, which was the gravitational centre for the triangle. This point is called the centroid. 

No homework tonight, and you won’t need your textbooks tomorrow as we’ll be focusing on literacy work. 

MPM2D1-01 Finding altitudes 2016-10-05

We wrapped up your area work (on the chart paper), and then learned to find an altitude given the coordinates of the vertices of a triangle.

If you have triangle ABC with base AB , the altitude from C can be found using the following steps:

  • Find the slope of AB
  • Find the slope of the altitude (negative reciprocal of the slope of AB since it’s perpendicular)
  • Find the equation of the line through AB
  • Find the equation of the altitude line

In the example we did today we also found the point D which was the intersection of the altitude with the base. For that we needed to solve the system of equations for those two lines.

Here are some helpful videos:

MPM2D1-02 Analytic Geometry: Finding perimeter and area of a quadrilateral 2016-10-03

We went over a couple of homework questions, then I gave the following instructions (verbally) to you in groups of 4-5:

  • Draw a set of axes on graph paper (we used chart paper)
  • Plot a point in each quadrant so that the quadrilateral formed by connecting adjacent quadrants’ points is NOT a nice parallelogram/rectangle/etc.
  • Calculate the perimeter and area of your quadrilateral.

All of the groups were able to calculate perimeter, but area proved to be much more challenging. By the end of the period a few groups had a plan, and at least one had completed the problem.

Tomorrow we’ll see the solutions, and I’ll show you how to use the technique that you all wanted to use (finding the altitude of a triangle).

No homework tonight!

MPM2D1-01 Length of a Line Segment 2016-10-03

We learned how to find the length of a line segment. That required us to remember how the Pythagorean Theorem works (just for right triangles!), and how radicals work (square roots, like \sqrt{13} ).

In the end, we settled on this formula:

|AB| = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}

I assigned Page 77 #1-8 for homework and gave you about 20 minutes in class to work on it. Finish it tonight, please!