SOLUTION: the distance between points M(3,5) and N(8,a) is 13.find the value of a.

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Question 466593: the distance between points M(3,5) and N(8,a) is 13.find the value of a.
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
M(3,5) and N(8,a) is 13

13= sqrt((3-8)^2+(5-a)^2)
13=sqrt(25+25-10a+a^2)
13=sqrt(50-10a+a^2)
square the equation
169 = a^2-10a+50
a^2-10a-119=0
Find the roots of the equation by quadratic formula

a= 1 b= -10 c= -119

b^2-4ac= 100 - 476
b^2-4ac= 576
sqrt%28576%29= 24
x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=( 10 + 24 )/ 2
x1= 17
x2=( 10 -24 ) / 2
x2= -7
a=17 OR -7