Question

In the question, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice.


Assertion (A): In the given figure, if P is the midpoint of AB, then the value of m is 3.
Reason (R): Th​​​e coordinates of the midpoint of a line formed by joining two points $(x_1,y_1)and(x_2,y_2)$ are $(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$.

(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.

[ 1 Mark ]

Answer 1

Answer: (A)

We know that th​​​e coordinates of the midpoint of a line formed by joining two points $(x_1,y_1)and(x_2,y_2)$ are $(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$.


Here, $x_1=m,x_2=5,y_1=2and{y}_2=-6$.

Let the coordinates of the point P be (x, y).

$(x,y)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

$(4,-2)=(\frac{m+5}{2},\frac{2+(-6)}{2})$

$\Rightarrow 4=\frac{m+5}{2}$

$\Rightarrow m+5=8$

$\therefore m=3$


Hence, both assertion (A) and reason (R) are true, and reason (R) is the correct explanation of assertion (A).
[1 marks]