Question

$A\equiv (a,b),B\equiv (a+2,b+3)$ and $C\equiv (a+7,b+6)$ are the vertices of $△ABC$. Mid-point $P$ of $AB$ lies on y-axis and the mid-point $Q$ of $AC$ lies on x-axis. $R$ is the midpoint of $BC$. Then match the coordinates of the point mentioned in List 1 with List 2

Answer 1

$P$ is mid point of $AB$, so coordinate of $P$ is $(a+1,\frac{2b+3}{2})$
It lies on y-axis $\Rightarrow a+1=0\Rightarrow a=-1$
$Q$ is mid point of $AC$, so coordinate of $Q$ is $(\frac{2a+7}{2},b+3)$
It lies on x-axis $\Rightarrow b+3=0\Rightarrow b=-3$
$R$ is mid point of $BC$, so coordinate of $R$ is $(\frac{2a+9}{2},\frac{2b+9}{2})$
Therefore,
A) $P$ is $(0,\frac{-3}{2})$
B) $Q$ is $(\frac{5}{2},0)$
C) Centroid of $△ABC$ where $A\equiv (-1,-3),B\equiv (1,0)$ and $C\equiv (6,3)$
Is $(\frac{-1+1+6}{3},\frac{-3+0+3}{3})=(2,0)$
D) Centroid of $△PQR$ where $P\equiv (0,-3/2),Q\equiv (\frac{5}{2},0)$ are $R\equiv (\frac{7}{2},\frac{3}{2})$
is $(2,0)$