Given the points A(a,3), B(-2,1) and C(3,2), what is the possible values of a if the length of AB is twice the length of BC?

1 Answer
Jan 27, 2018

#a=-12" or "a=8#

Explanation:

#"calculate the lengths of AB and BC using the"#

#color(blue)"distance formula"#

#•color(white)(x)d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)#

#AB=sqrt((a+2)^2+(3-1)^2)=sqrt((a+2)^2+4)#

#BC=sqrt((3+2)^2+(2-1)^2)=sqrt(25+1)=sqrt26#

#"equating "AB=2BC#

#rArrsqrt((a+2)^2+4)=2sqrt26#

#color(blue)"squaring both sides"#

#rArr(a+2)^2+4=104#

#rArr(a+2)^2=104-4=100#

#color(blue)"take the square root of both sides"#

#rArra+2=+-10larrcolor(blue)"note plus or minus"#

#rArra=-2+-10#

#rArra=-2-10=-12 or "a=-2+10=8#