Question

Given: Line segment with endpoints A(‒6,6) and B(6,‒3). Prove: If the coordinates of Y is (2,0), prove that Y is two-thirds of the way from A to B?

Answer 1

see explanation.

Explanation:

Use the distance formula: `d = sqrt((x_2-x_1)^2 + (y_2-y_1)^2)` to find the length `AY and YB`
`AY=sqrt((2-(-6)^2)+(0-6)^2)=sqrt(8^2+6^2)=sqrt100=10` units
`YB=sqrt((6-2)^2+(-3-0)^2)=sqrt(4^2+3^2)=sqrt25=5` units
`=> AY:YB=10:5=2:1`
`=> AY:AB=2:3`
`=> AY=2/3*AB`