Finding the terminal points at Analytic Geometry Forum

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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Jhun Vert Sun, 07/30/2017 - 15:46

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.

Anonymous (not verified) Tue, 12/21/2021 - 22:06

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

Jhun Vert Wed, 12/22/2021 - 00:59

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.

Anonymous (not verified) Wed, 12/22/2021 - 02:22

Got it now thank you!

naome (not verified) Mon, 04/25/2022 - 20:34

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

Jhun Vert Mon, 05/02/2022 - 20:14

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

Finding the terminal points

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