Question

Assertion: The coordinates of A and B are (1, 2) and (2, 3), respectively. If R is a point on AB such that AR : RB = 4 : 3, then coordinates of R will be `(11/7,  18/7)`.

Reason: The coordinates of the mid-point of line segment joining (x₁, y₁) and (x₂, y₂) are `((x_1 + x_2)/2, (y_1 + y_2)/2)`.

Options

• Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A).

• Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).

• Assertion (A) is true, but Reason (R) is false.

• Assertion (A) is false, but Reason (R) is true.

Answer 1

Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).

Explanation:

⇒ The assertion is true because using the section formula with AR : RB = 4 : 3 yields,

R = `((3 xx 1 + 4 xx 2)/7, (3 xx 2 + 4 xx 3)/7)`

= `(11/7, 18/7)`

⇒ Reason is true by using the midpoint formula, but not the correct explanation, since the midpoint is the special case m : n = 1 : 1.