Question

1. The distance of the point (1, 2) from the mid-point of the line segment joining the points (6, 8) and (2, 4) is 5 units.
2. y-axis divides the line segment joining A(−4, 6) and B(8, −3) in the ratio 2 : 1.

Options

• Only (i)

• Only (ii)

• Both (i) and (ii)

• Neither (i) nor (ii)

Answer 1

Only (i)

Explanation:

⇒ The midpoint of (6,8) and (2,4) is:

`((6 + 2)/2, (8 + 4)/2)` = (4, 6)

Distance from (1, 2) to (4, 6):

= `sqrt(3^2 + 4^2)`

= 5,

So (i) is true.

⇒ For (ii), the y-axis meets AB at x = 0, giving t = `1/3`, so AP : PB = 1 : 2, not 2 : 1, hence (ii) is false.