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The line $x + y = 10$ cuts the segment joining A(2, 3) and B(8, 11) at P. In what ratio does P divide AB?

Competition practiceGeometry

A5 : 9
B9 : 5
C1 : 1
D5 : 4

Step-by-Step Solution

Let AP : PB =

k

: 1, so

P = (\frac{8 k + 2}{k + 1}, \frac{11 k + 3}{k + 1})

. On the line:

19 k + 5 = 10 (k + 1)

, so

k = \frac{5}{9}

and the ratio is 5 : 9.

Answer: A) 5 : 9

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