Question

Assertion :Vertices of a triangle are $A(a,b),B(a+1,b-2),C(a-2,b+1)$. If the origin is shifted to the centroid of the triangle without rotation of axes, coordinates of $A$ in the new system of coordinates are $(\frac{1}{3},\frac{1}{3})$ Reason: Centroid of an equilateral triangle is equidistant from its vertices

• 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 B Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

Assertion:
Centroid of $ABC$ is $(a-\frac{1}{3},b-\frac{1}{3})$
If $(X,Y)$ are the new coordinate of $A$, then
$X=a-(a-\frac{1}{3})=\frac{1}{3}Y=b-(b-\frac{1}{3})=\frac{1}{3}$
Hence, it is true.
Reason: is also true but is not a correct explanation for assertion.