Question

Assertion :If $(0,3)$, $(2,2)$ & $(-2,1)$ be the mid points of the sides of a triangle, then centroid of the original triangle is $(0,2)$. Reason: Centroid of the original triangle & triangle obtained by joining the mid points of the sides of the triangle is (unaltered) same.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

Let the vertices be ${(x}_1,y_1),{(x}_2,y_2),{(x}_3,y_3)$

Centroid of $△=(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3})$

Midpoints of triangle are $(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}),(\frac{x_2+x_3}{2},\frac{y_2+y_3}{2})(\frac{x_1+x_3}{2},\frac{y_1+y_3}{2})$

Hence centroid is $\frac{\frac{x_1+x_2}{2}+\frac{x_2+x_3}{2}+\frac{x_1+x_3}{2}}{3},\frac{\frac{y_1+y_2}{2}+\frac{y_2+y_3}{2}+\frac{y_1+y_3}{2}}{3}$

$=\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3}$

We observe that $△$ formed by midpoints also has same centroid.

$\therefore$ Centroid of original $△=(\frac{0+2+-2}{3},\frac{3+2+1}{3})$

$=(0,2)$

So both assertion and reason are explained