1. Day 7: Orthocentres Unit 3: Coordinate Geometry
Did you know that the longest street in the world is in Toronto?
(Yonge St. is 1896 km long)

2. Learning Goals
To be able to calculate the orthocentre of a triangle

3. Orthocentre
The point of intersection of the three altitudes of a triangle

4. Draw a triangle with vertices A (0, 4), B (−2, 2) and C (6, 2)
Draw a triangle with vertices A (0, 4), B (−2, 2) and C (6, 2). Sketch the altitudes. Find the coordinates of the orthocentre.

5. Draw a triangle with vertices A (0, 4), B (−2, 2) and C (6, 2)
Draw a triangle with vertices A (0, 4), B (−2, 2) and C (6, 2). Sketch the altitudes. Find the coordinates of the orthocentre. Step 1: Find the equation of one of the altitudes.

6. Draw a triangle with vertices A (0, 4), B (−2, 2) and C (6, 2)
Draw a triangle with vertices A (0, 4), B (−2, 2) and C (6, 2). Sketch the altitudes. Find the coordinates of the orthocentre. Step 2: Find the equation of another altitude.

7. Draw a triangle with vertices A (0, 4), B (−2, 2) and C (6, 2)
Draw a triangle with vertices A (0, 4), B (−2, 2) and C (6, 2). Sketch the altitudes. Find the coordinates of the orthocentre. Step 3: Use substitution or elimination to find the point of intersection.

8. Orthocentre
The point of intersection of the three altitudes of a triangle
Calculate the equations of two of the altitudes
Solve using substitution

9. Success Criteria
I CAN use the equations of the altitudes to find the orthocentre of a triangle

10. To Do…
Worksheet
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