Question

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?

Answer 1

`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`