Question

The line segment joining the points (5, −4) and (2, 2) is divided by the points Q in the ratio 1 : 2. Does the line x – 2y = 0 contain Q?

Answer 1

Given, the line segment joining the points (5, −4) and (2, 2) is divided by the point Q in the ratio 1 : 2.

Co-ordinates of the point Q are

`((1 xx 2 + 2 xx 5)/(1 + 2),(1 xx 2 + 2 xx (-4))/(1 + 2))`

= `((2 + 10)/3, (2 - 8)/3)`

= `(12/3, (-6)/3)`

= (4, –2)

Substituting x = 4 and y = –2 in the given equation, we have:

L.H.S. = x − 2y

= 4 − 2(−2)

= 4 + 4

= 8 ≠ R.H.S.

Hence, the given line does not contain point Q.