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Find the rati...

Question

Find the ratio in which 𝑷(𝟒, 𝒎) divides the line segment joining the points 𝑨(𝟐, 𝟑) and 𝑩(𝟔, −𝟑). Also, find 𝒎.

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Solution

Let P divide the line segment AB in the ratio k:1.
But the coordinate of P are (4, m). Hence,
Hence, P divides AB in the ratio 1:1.
So, applying k = 1, we get:

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