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