Plot all points that are 3 units from the x-axis and 3 units from (5,4). how many did you find?

All points 3 units from the x axis are on y=3 and y=-3

the distance formula is
ok, one point is (5,4) and the other is (x,3) or (x,-3), find both

for (x,3)   (the ones on y=3)




squaer both sides
9=x²-10x+26
minus 9
0=x²-10x+17
factor
we can't
using quadratic formula
x=5-2√2 or 5+2√2

for (x,-3)




squaer both sides
9=x²-10x+74
0=x²-10x+65
solving using quadratic formula we get a false statment
no points

so the 2 points are
and

It would be 18 cm