SOLUTION: Find the value of "a" if the points are the indicated distances apart. (2,a) and (-3,-2) when d = square root of 34

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Question 59974This question is from textbook Alegbra Concepts and Applications
: Find the value of "a" if the points are the indicated distances apart.
(2,a) and (-3,-2) when d = square root of 34 This question is from textbook Alegbra Concepts and Applications

Found 2 solutions by funmath, jenrobrody:
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
Find the value of "a" if the points are the indicated distances apart.
(2,a) and (-3,-2) when d = square root of 34
The distance formula is highlight%28d=sqrt%28%28x2-x1%29%5E2%2B%28y2-y1%29%5E2%29%29
(x1,y1)=(2,a), (x2,y2)=(-3,-2) d=sqrt%2834%29
sqrt%2834%29=sqrt%28%28-3-2%29%5E2%2B%28-2-a%29%5E2%29
%28sqrt%2834%29%29%5E2=%28sqrt%28%28-5%29%5E2%2B%28-2-a%29%5E2%29%29%5E2
34=%28-5%29%5E2%2B%28-2-a%29%5E2
34=25%2B4%2B4a%2Ba%5E2
34=29%2B4a%2Ba%5E2
-34%2B34=-34%2B29%2B4a%2Ba%5E2
0=-5%2B4a%2Ba%5E2 Set = to 0
a%5E2%2B4a-5=0 factor
(a+5)(a-1)=0 Use the zero product property.
a+5=0 and a-1=0
a+5-5=0-5 and a-1+1=0+1
a=-5 and a=1
There's two possibilities. Use the distance formula and see that both have a distance of sqrt%2834%29.
Happy Calculating!!!

Answer by jenrobrody(19) About Me  (Show Source):
You can put this solution on YOUR website!
(2,a) and (-3,-2) when d = square root of 34
d+=+sqrt%28+%28x1-x2%29%5E2+%2B+%28y1-y2%29%5E2%29
sqrt%2834%29=sqrt%28%282-%28-3%29%29%5E2%2B%28a-%28-2%29%29%5E2%29
square both sides:
34=5%5E2%2B%28a%2B2%29%5E2
34=25%2Ba%5E2%2B4a%2B4
0=a%5E2%2B4a-5
0=%28a%2B5%29%28a-1%29
so either a+5=0 or a-1=0
which gives two values for a: -5 and 1