Name______________________

MPM2D: Analytic Geometry: Problem Solving

So far, you have learned a number of algebraic techniques that are useful when solving problems using lines, points, triangles, circles, etc. These techniques are listed below, and are part of your toolbox!

These “tools” can be used to solve many interesting and useful problems!

The sequence of steps used to solve a problem is called the algorithm.

Example: Page 195 #12

Find the coordinates of the centroid of a triangular metal part with vertices at A(12,18), B(18,6), and C(3,12).

Note: the centroid is the intersection of the medians.

Homework Assignment

1. Follow the Algorithm in the previous example, and solve the problem.

Label the diagram as you go.

2. For each of the following problems

i) Draw a labelled sketch

ii) Write an algorithm to solve the problem (refer to tools from the toolbox)

** DO NOT SOLVE THE PROBLM JUST WRITE THE ALGORITHM**

Page 195 # 13

Find the orthocenter of the triangle with vertices at P(-1,5), Q(7,2), and R(-1,-4).

( The orthocenter is the intersection point of the altitudes of a triangle)

Page 196 # 15

An iceberg is situated off the coast of Newfoundland at map coordinates (40,10). A cruise ship is at (-20, 60) and heading straight for (50,-10). If the cruise ship maintains the same course, how close to the iceberg will the ship get?