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Division of an interval in a given ratio. Suppose given an interval М1М2. Let us find the coordinates a of point М on the interval for which .

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Division of an interval in a given ratio. Suppose given an interval М1М2. Let us find the coordinates a of point М on the interval for which .

Division of an interval in a given ratio. Suppose given an interval М1М2. Let us find the coordinates a of point М on the interval for which . - раздел Образование, Ne Compose The Vectors ...

Compose the vectors and .

M₂(x₂,y₂)

M(x,y)

M₁(x₁,y₁)

0 x

It is known from vector algebra that the condition for two vectors to be collinear is the proportionality of their respective coordinates:

From the first fraction we obtain

; ; .

This gives the x coordinate; y is found in a similar way:

; .

To obtain a formula for the midpoint of the interval, we take l=1:

; .

Example. Given the two points М₁(–2;4) and М₂(6;2), find the midpoint of the interval М₁, М₂.

М₁,

М₂ .

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The distance between two points Let us find the distance between two points М and М in the plane... Example Find the distance between the two points А and... Using the above formula we obtain...

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