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