Question

Find two points that divide the line segment AB into 3 equal parts

Answer 1

A (1,-3)
B (7,21)

Answer 2

Find a parametrization on that line segment then let t=1/3 and 2/3.

Answer 3

what is parametrization?

Answer 4

It's another way of writing the equation of a line segment. In this case, the required parametrization is \(x=(1-t)+7t, y= (1-t)(-3)+21t\). Now let t=1/3 then t=2/3.

Answer 5

so the two points will be (3,5) and (5,13)?

Answer 6

however, i don't quite understand how do you turn the coordinates to the parametrization of the line.

Answer 7

Or is there an easier way because I have a bunch of other similar questions.

Answer 8

Denote the vertical difference by \(\Delta y\) and the horizontal difference by \(\Delta x\).
Since you need to divide the line into 3 parts, get \(\large a=\frac{\Delta y}{3} \text{and } b=\frac{\Delta x}{3}\).
Add these values successively to the lower left point: \((1+a,-3+b), (1+2a, -3+2b)\).
Just realized this easier solution now.

Answer 9

Oh, i see.

Answer 10

if I use the second way, i have different answers

Answer 11

Oops. I switched a and b in the 2nd line. It should be \(\Large a=\frac{\Delta x}{3}, b=\frac{\Delta y}{3}\).

Answer 12

Did I do something wrong?