How do you find a possible value for a if the points (7,5), (-9,a) has a distance of #d=2sqrt65#?

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Answer 1 · 2017-03-19T04:06:20

#a = {3, 7}#

To solve for the value of #a#, we will use the distance formula:

#"distance" = sqrt(("change in x")^2 + ("change in y")^2)#

The change in #x# is the difference between x-coordinates:

#7 - (-9) = 7 + 9 = 16#

The change in #y# is the difference between y-coordinates:

#5 - a#

Now, plug these values into the distance formula:

#"distance" = sqrt(("change in x")^2 + ("change in y")^2)#

#2sqrt(65) = sqrt((16)^2+(5-a)^2)#

Squaring both sides gives:
#260 = (16)^2+(5-a)^2#
#260 = 256 + (5-a)^2#

#4 = (5-a)^2#
#+-2 = 5-a#
#a = 5 +-2#

Therefore, #a# could be either 3 or 7.