Assertion (A) : If the co-ordinates of the mid-points of the sides $A B$ and $A C$ of $ riangle A B

Question

Assertion (A) : If the co-ordinates of the mid-points of the sides $A B$ and $A C$ of $	riangle A B C$ are $D(3,5)$ and $E(-3,-3)$ respectively, then $B C=20$ units.\ Reason (R) : The line joining the mid points of two sides of a triangle is parallel to the third side and equal to half of it.\

Professor PC Thomas Classes · Answer

(a) : Length of $D E=\sqrt{(3+3)^{2}+(5+3)^{2}}=\sqrt{6^{2}+8^{2}}$\ $=10$ units\ We know, line joining the mid points of two sides of a triangle is parallel to third side and equal to half of it.\ So, $D E=\frac{1}{2} B C \Rightarrow B C=20$ units.\ Hence, both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).\