Day 7: Orthocentres Unit 3: Coordinate Geometry

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Presentation transcript:

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)

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

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

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.

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.

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.

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.

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

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

To Do… Worksheet Check the website daily for updates, missed notes, assignment solutions www.mrsmccrum.weebly.com New: note outline available the night before (completed note will no longer be posted)