Investigating in Grade 10

Que remarquez-vous?  Que voulez vous savoir?

Grade 10s were investigating a sprinkler today.  If the sprinkler can spray a maximum of 10 meters, and we want to make sure each point labelled on the grid gets wet, where should we put the sprinkler?  


We listed things we know….like sprinklers can spray in a circle, and that the sprinkler should be in the middle somewhere…but which “middle”?  How can we find a spot that is equidistant to all points?

We know we can draw the “médiatrice” (perpendicular bisector) and that will show us all the points that are equidistant to the segment’s endpoints.  We drew a lot of them, and noticed that they intersect!

So we’d put the sprinkler there!

Next we looked at each point and made sure that it really was the same distance from the sprinkler.  We used the pythagorean theorem or the distance formula.  We called the sprinkler point (0,0)

Next we looked for more points that are also on the circle.  We know that (10,0) (0,10) (-10,0) (0,-10) are all 10 units from the center, as are all the variations with 6 and 8.

Finally we can say that any point in the circle will be wet, and any point outside the circle will remain dry.

we made a general equation for the circle, centered at (0,0) using the distance formula.

And then we used the formula to help us calculate the y value for a point that has an x value of 9.

We ended up with 2 options, one is positive and one is negative, which makes sense when you look at the picture of the circle.