Question

I need the answer to question three and four please

Answer 1

3a and b) The sprinkler is on (6,2) and the blade of grass is on (x,y). We need to find the distance between those two points and check whether that distance is less or equal to 5 (in that case, the blade of grass will get wet).

We can find the distance between two points by using the formula:

`d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}`

Where the distance we measure is between the points (x_1,y_1) and (x_2,y_2)

Then, in our case, the formula gets reduce to:

`5=\sqrt[]{(x-6)^2+(y-2)^2}`

This is the equation we are looking for in part b.

4) If the sprinkler is at (a,b) we simply need to substitute (6,2) for (a, b) in the expression above. Moreover, the distance the sprinkler can reach now is equal to r, we need to change 5 for r too.

We end up with the following expression:

`r=\sqrt[]{(x-a)^2+(y-b)^2}`

This is the equation we are looking for in part 4, and that's the equation of a circumference centered at (a,b) and radius equal to r.