SOLUTION: The distance between the points A and B is \sqrt{34}. If A = (a,4) and B = (-4,5), then find the sum of all possible values of a.

Algebra.Com
Question 1209010: The distance between the points A and B is \sqrt{34}. If A = (a,4) and B = (-4,5), then find the sum of all possible values of a.
Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
The distance between the points A and B is \sqrt{34}. If A = (a,4) and B = (-4,5),
then find the sum of all possible values of a.
~~~~~~~~~~~~~~~~~~~~~~~ 

From the condition, we have this distance formula

    34 =  + ,

or

    34 =  + ,

    34 =  + 1,

    33 = ,

    a + 4 = +/- ,

     = -4 +- .


Thus   +  = -4 +  -4 -  = -8.


ANSWER.  The sum of all possible values of "a" is -8.

Solved.



Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

d = distance from A to B
Distance formula

Plug in the given distance

Plug in (x1,y1) = (a,4) and (x2,y2) = (-4,5)





Square both sides

Let's replace 'a' with x to get

That rearranges to which I'll let the student handle the scratch work.

Since the leading coefficient is 1, the roots p and q add to the negative of the x coefficient (refer to Vieta's Formulas; specifically the quadratic version)

Therefore we determine p+q = -8 which is the final answer
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