Question

Assertion (A): The ratio in which the line segment joining (2, -3) and (5, 6) internally divided by x axis is 1:2.

Reason (R): as formula for the internal division is \((\frac{mx_2 +nx_1}{m+n},\frac{my_2 +ny_1}{m+n})\)

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

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

(c) Assertion (A) is true but Reason (R) is false. 

(d) Assertion (A) is false but Reason (R) is true.

Answer 1

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

The Formula of interal division is

\((\frac{mx_2 +nx_1}{m+n},\frac{my_2 +ny_1}{m+n})\)

Hence, our reason (R) is true.

Let x-axis divides line segment joining points A(2,-3) and B(5,6) internally in the ratio K : 1.

∴ y -coordinate of that point should be zero because y-coordinate of any point on x-axis is zero.

∴ \(\frac{6k-3}{k+1}=0\) 

(By putting m = k, n = 1, y₂ = 6 & y, = -3 in equation (1))

⇒ 6k - 3 = 0

⇒ k = 3/6 = 1/2

⇒ k/1 = 1/2

⇒ k : 1 = 1 : 2

Hence, x-axis divides line segment joining points (2,-3) & (5,6) internally in the ratio 1 : 2. 

Hence, our assertion and reason both are true and reason is correct explanation of assertion.