Question #9c2e8

1 Answer
Jim H
Jan 16, 2018

Notice that the two points have the same #x#-coordinate.

Explanation:

Using geometry

So only the #y#-coodinates will be different.

All of the points lie on the same vertical line.
The points on the vertical axis whose distance to #(0.-6)# is #8# can be found by adding and subtracting #8# to/ from #-6#

The points are #(4,2)# and #(4,-14)#

Using the distance formula

The distance between the points is

#sqrt((x_2-x_1)^2+(y_2-y_1)) = sqrt((4-4)^2+(y-(-6))^2)#

# = sqrt((y+6)^2)#

We want the distance to be #9#, so we will solve

#sqrt((y+6)^2) = 8# #" "# (square both sides)

#(y+6)^2=64# #" "# (take square roots -- remember #+-#

#y+6 = +-8# #" "# finish solving for #y#

#y+6=8# then #y=2#

#y+6=-8# then #y=-14#

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