Question

The points $A\equiv (2,3)$, $B\equiv (3,5)$, $C\equiv (7,7)$ and $D\equiv (4,5)$ are such that

• A. $ABCD$ is a parallelogram
• B. $A,B,C$ and $D$ are collinear
• C. $D$ lies inside the $△ABC$
• D. $D$ lies on the boundary of the $△ABC$.

Answer 1

Answer: (C)

$D$ lies inside the $△ABC$

Given, $A=(2,3),B=(3,5),C=(7,7),D=(4,5)$

Since $\frac{2+3+7}{3}=4$, $\frac{3+5+7}{3}=5$

D$(4,5)$ is the centroid of the triangle $ABC$

and hence lies inside it.