SOLUTION: Find the point on the positive y-axis that is a distance 5 from the point P(3,4). The answer is multiple choice. a. A(0,6) b. A(0,8) c. A(6,0) d. A(8,0)

Find the point on the positive y-axis that
is a distance 5 from the point 
P(3,4). The answer is multiple choice. 
a. A(0,6)
b. A(0,8)
c. A(6,0)
d. A(8,0)

Every point on the y-axis has 0 as its 
x-coordinate, which immediately
rules out c and d.  

So let the desired point be A(0,y)

Use the distance formula:
     ___________________
d = Ö(x2-x1)² + (y2-y1)²

(x1,y1) = (3,4), (x2,y2) = (0,y), d = 5

     ___________________
5 = Ö(0 - 3)² + (y - 4)²
     ________________
5 = Ö(-3)² + (y - 4)²
     ____________
5 = Ö9 + (y - 4)²

Square both sides:

25 = 9 + (y - 4)²

16 = (y - 4)²

Take square roots of both sides

±4 = y - 4

4 ± 4 = y

Using the +, y = 8
Using the -, y = 0

So there are two points on the x-axis
which are 5 units from P(3,4). They
are (0,8) and (0,0).  The only one
listed is (0,8). So the correct choice
is b.

Edwin