How do you find the value of a given the points (4,a), (1,6) with a distance of 5?

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Answer 1 · 2016-07-27T12:18:46

#a = 10 or a=2#

Use the distance formula and substitute the values you know:

#|AB| = sqrt[(x_2-x_1)^2 +(y_2-y_1)^2]#

#5 = sqrt[(4-1)^2 +(a-6)^2#

#5 = sqrt[3^2 +(a-6)^2]" square both sides"#

#25 = 9 + (a^2 -12a +36)" quadratic = 0"#

#0 = a^2 -12a +36 +9 -25#

#0 = a^2 -12a +20#

Now solve the quadratic to find two possible answers for a.

#0= (a-10)(a-2)#

This gives the possible answers for a as;
#a = 10 or a=2#