In what ratio the line y - x + 2 = 0 divides the line joining the points (3, -1) and (8,9)

1) 1 : 2

2) 2 : 1

3) 2 : 3

4) 3 : 4

Solution:

Let the line y – x + 2 = 0 divide the line joining the points A(3, -1) and B(8, 9) in the ratio k:1.

Let C(x, y) be the point of intersection of these two lines.

Then by section formula

x = (mx2+nx1)/(m+n)

y = (my2+ny1)/(m+n)

Here (x1, y1) = (3, -1)

(x2, y2) = (8, 9)

m:n = k:1

So x = (8k + 3)/(k+1)

y = (9k – 1)/(k+1)

The point C lies on the line y – x + 2 = 0

So (9k – 1)/(k+1) – (8k + 3)/(k+1) + 2 = 0

=> (9k – 1 – 8k – 3 + 2k + 2)/(k+1) = 0

=> (3k – 2)/(k+1) = 0

=> 3k – 2 = 0

=> k = 2/3

So the required ratio is 2:3.

Hence option (3) is the answer.

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