In what ratio does the line x – y – 2 = 0 divide the line segment joining the points A (3, –1) and B(8, 9)?
The line segment joining any two points (x1, y1) and (x2, y2) y2 is given as:
⇒
⇒ y + 1 = 10/5 (x-3)
⇒ y + 1 = 2(x-3)
⇒ y + 1 = 2x – 6
⇒ 2x – y = 7..eq(1) is the equation of line segment.
Now, we have to find the point of intersection of eq (1) & the given line: x – y- 2 = 0
2x – y = 7
& x – y – 2 = 0
2x – 7 = x – 2
⇒ x = 7- 2
⇒ x = 5
And, y = 3
Let us say this point divides the line segment in the ratio of k1:k2
Then,
⇒ 5k1 + 5k2 = 8k1 + 3k2
⇒ 5k1 - 8k1 + 5k2 - 3k2= 0
⇒ -3k1 + 2k2 = 0
⇒