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ryzh [129]
3 years ago
12

GEOMETRY *image is attached above*

Mathematics
1 answer:
Keith_Richards [23]3 years ago
6 0

Answer:

(-9.5, -4)

Step-by-step explanation:

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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