The segment joining (1 -3) and (4 -6) is extended a distance equal to one sixth of its own length. find the terminal points.
How to solve this problem. I need the whole SOLUTION. THANKS

Consider the original line (green) to be composed of six parts so that extensions are 1 part each. From (1, -3) to Extension point 1 is -1 part and from (1, -3) to (4, 6) is 6 parts, hence, r = -1/6. Do similarly to Extension Point 2.

There are two possible extension points as shown. Use the following formulas to find these points:

$x = x_1 + r(x_2 - x_1)$

$y = y_1 + r(y_2 - y_1)$

Note:

(

x_{1},y_{1}) = (1, -3) and(

x_{2},y_{2}) = (4, -6)For extension point 1, use

r= -1/6; and for extension point 2, user= 7/6.How did you find the r=-1/6 and 6/7 then?

Consider the original line (green) to be composed of six parts so that extensions are 1 part each. From (1, -3) to Extension point 1 is -1 part and from (1, -3) to (4, 6) is 6 parts, hence,

r= -1/6. Do similarly to Extension Point 2.Got it now thank you!

Why is it -1 for extension point 1 sir ? why is the whole parts are still six if there is this extension 1 sir?

opposing directions are of different signs. If you consider upward to be negative, downward is positive and vice versa.

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