Given the ratio a:b (a to b) of two segments formed by a point of partition, and the endpoints of the original segment, we can calculate the point of partition using this formula:

$( \frac{a }{a + b} (x_{2} - x_{1}) + x_{1}, \frac{a}{a + b} (y_{2} - y_{1})+y_{1})$ .

Given two endpoints of the original segment

→ (-10, -8) [(x₁, y₁)] and (-8, 8) [(x₂, y₂)]

Along with the ratio of the two partitioned segments

→ 1 to 3 = 1:3 [a:b]

Formed by the point that partitions the original segment to create the two partitioned ones

→ (x?, y?)

We can apply this formula and understand how it was derived to figure out where the point of partition is.

Here is the substitution:

x₁ = -10

y₁ = -8

x₂ = -8

y₂ = 8

a = 1

b = 3

$( \frac{a }{a + b} (x_{2} - x_{1}) + x_{1}, \frac{a}{a + b} (y_{2} - y_{1})+y_{1})$ . →

$( \frac{(1) }{(1) + (3)} ((-8) - (-10)) + (-10), \frac{(1)}{(1) + (3)} ((8) - (-8))+ (-8))$ →

$( \frac{1}{4} ((-8) - (-10)) + (-10), \frac{1}{4}((8) - (-8)) + (-8))$ →

$( \frac{1}{4} (2) + (-10), \frac{1}{4}(16) + (-8))$ →

$( (\frac{1}{2}) + (-10), (4) + (-8))$ →

$( (-\frac{19}{2}), (-4))$ →

$( -\frac{19}{2}, -4)$ →

* $( -9.5, -4)$ *

Now the reason why this

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