SOLUTION: well its a two part question i answered a already but am finding it impossible to answer b i was hoping you could help me out in the first part you had to show that p (4,2) was equ

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Question 201967: well its a two part question i answered a already but am finding it impossible to answer b i was hoping you could help me out in the first part you had to show that p (4,2) was equidistant from a (9,2) and b (1,6). i did this by graping the points and then using the distance formula from a to p and b to p which when rounding p to b is equidistant. however the second part says this:
if (2,k) is equidistant from a and b find the value of k.
thanks so much for any help you could provide me with.
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
use the distance formula and set the distances equal

sqrt[(9-2)^2 + (2-k)^2] = sqrt[(1-2)^2 + (6-k)^2]

squaring and expanding ___ 49 + 4 - 4k + k^2 = 1 + 36 - 12k + k^2

subtracting k^2-12k+53 ___ 8k = -16

dividing by 8 ___ k = -2