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This group found the equations of all three sides of the right triangle, and when they tried to find the equation of the altitude of one of the perpendicular sides, they realized it was the same as the equation of the other perpendicular side....and then they realized where the Orthocentre was.

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I liked that this group found the x-value of the Orthocentre and realized that it was at the 90 degree vertex. "It's a right triangle so of course the perpendicular sides are the altitudes to each other!"

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This group's answer is in the top left corner.

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Day5 - What is a Orthocentre of a Triangle?

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Day5 - What is a Orthocentre of a Triangle?

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The Orthocentre is where the 3 altitudes of a triangle intersect.
A triangle is created by connecting (2,8), (-2,2) and (7,-4).
Find the coordinates of the Orthocentre.

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Do you see the answer in the bottom right corner? (-2,2), the vertex at the 90 degree! So the Orthocentre of a right triangle is at the vertex of the 90 degree angle. Why is that?

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Good start! Found one altitude equation and started on the second. What's next?

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Day4 - Find the Co-ordinates of the Centroid Task (Solution pg 2)

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Day4 - Find the Co-ordinates of the Centroid Task (Solution pg 2)

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Day4 - Find the Co-ordinates of the Centroid Task (Solution pg 1)

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Day4 - Find the Co-ordinates of the Centroid Task (Solution pg 1)

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Day4 - Find the Co-ordinates of the Centroid Task

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Day4 - Find the Co-ordinates of the Centroid Task

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Day4 - Find the Co-ordinates of the Centroid Task

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Day4 - Find the Co-ordinates of the Centroid Task

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Day3 - Make a scalene right triangle... 

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Day3 - Make a scalene right triangle... 

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Now make you right triangle into an isosceles triangle.

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Now find the perimeter, area and interior angles.

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with the line segment from(-2,-2) to (4,0) as one of the perpendicular sides.

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Lines that meet at a 90 degree angle have slopes that are negative reciprocal of each other. Meaning you flip their rise and run and if one of the slopes is positive, the other one has to be negative.

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When the rise is negative it means you are going down or moving in the negative direction.
When the run is positive it means you are moving in the positive direction. But if the run is negative it means you are moving in the negative direction.

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There's a bunch of ways to write a negative fraction, but the last one below ends up being positive

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Day1 - What do you notice about this graph? cont....

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Day1 - What do you notice about this graph? cont....

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Here's what another group did.

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Day1 - What do you notice about this graph? cont....

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Day1 - What do you notice about this graph? cont....

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Here's what one group did to find where the lines meet.

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Day1 - What do you notice about this graph?

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Day1 - What do you notice about this graph?

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Students came up with some great answers!