# Finding the terminal points

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

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### There are two possible

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:
(x1, y1) = (1, -3) and
(x2, y2) = (4, -6)

For extension point 1, use r = -1/6; and for extension point 2, use r = 7/6.

### How did you find the r=-1/6

How did you find the r=-1/6 and 6/7 then?

### Consider the original line

In reply to by Anonymous (not verified)

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.

### Why is it -1 for extension

In reply to by Jhun Vert

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

In reply to by naome (not verified)

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