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
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#