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GEOMETRY

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GEOMETRY *image is attached above*-example-1
User Gnvk
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Answer:

(-9.5, -4)

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:


( (a )/(a + b) (x_(2) - x_(1)) + x_(1), (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


( (a )/(a + b) (x_(2) - x_(1)) + x_(1), (a)/(a + b) (y_(2) - y_(1))+y_(1)). →


( ((1) )/((1) + (3)) ((-8) - (-10)) + (-10), ((1))/((1) + (3)) ((8) - (-8))+ (-8))


( (1)/(4) ((-8) - (-10)) + (-10), (1)/(4)((8) - (-8)) + (-8))


( (1)/(4) (2) + (-10), (1)/(4)(16) + (-8))


( ((1)/(2)) + (-10), (4) + (-8))


( (-(19)/(2)), (-4))


( -(19)/(2), -4)

*
( -9.5, -4)*

Now the reason why this

User SampathKumar
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