Question:

5. Find the ratio in which point P(k, 7) divides the segment joining A(8, 9) and B(1, 2). Also find k .

Answer:

Let P (x, y) , A (x1, y1) and B (x2, y2) and be the given points.
Here, x = k, y = 7, x1 = 8, y1 = 9, x2 = 1, y2 = 2,
By Section formula y = (my2+ny1)/(m+n)
7 = m×2+n×9/(m+n)
7 = 2m+9n/(m+n)
7m+7n = 2m+9n
7m-2n = 9n-7n
5m = 2n
m/n = 2/5
Hence m:n = 2:5.
By Section formula, x = (mx2+nx1)/(m+n)
k = (2×1+5×8)/2+5
k = (2+40)/7
k = 42/7 = 6
Hence value of k is 6.
Hence P(6,7) divides the segment in the ration 2:5.

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