Determine a value for k so that the point (1,k) is the same distance from the line x= -2 as it is from the point (2,0).
Here is one way of doing this.
The point (1,k) is anywhere on the vertical line x=1.
The distance of vertical line (x=1) from the vertical line (x = -2) is 3 units.
The distance of (1,k) from (2,0) can be found by the distance formula.
So,
3 = sqrt[(1-2)^2 +((k-0)^2]
3 = sqrt[1 +k^2]
Square both sides.
9 = 1 +k^2
k^2 = 9 -1 = 8
k = +,-sqrt(8) = +,-2sqrt(2) --------answer.
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Check if (1, +,-2sqrt(2)) is 3 units away from (2,0):
d = sqrt[(1 -2)^2 +(+,-2sqrt(2) -0)^2]
d = sqrt[(1) +4(2)]
d = sqrt(9) = 3 ------it is, so, okay.