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

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 Click here to see ALL problems on Length-and-distance Question 466593: the distance between points M(3,5) and N(8,a) is 13.find the value of a.Answer by mananth(12270)   (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 = 24 x1=( 10 + 24 )/ 2 x1= 17 x2=( 10 -24 ) / 2 x2= -7 a=17 OR -7