Finding coordinates

[Jands1099]

 

[Jands1099]

 

[Deleted member 4993]

View attachment 21442

Where is the "question" or "?" here!

 

[Dr.Peterson]

View attachment 21445

Presumably you are supposed to find X, but you didn't show the instructions.

Are you aware that if B is some part of the way from A to C, then the same is true of its x- and y-components?

Please show what you've tried, so we can see what sort of help you need.

 

[pka]

View attachment 21442

I may give you a way of doing this that seems strange. But please try to see why it works.
The line segment is:
\(\ell (t) = (-1+6t,~4-7t)\) note that \(\ell(0)=(-1,4)~\&~\ell(1)=(5,-3)\) so \(\ell\left(\frac{1}{3}\right)=\left(1,\frac{5}{3}\right)\)

 

[HallsofIvy]

That seems more complicated than necessary! Instead of getting parametric equations for the line, think "similar triangles" which tell you that you can do the x and y coordinates separately. What number is 1/3 of the way from -1 to 5? What number is 1/3 of the way from 4 to -3?