Question

In the given figure, $LM$ is a line parallel to the $y$-axis at a distance of $3$ units. What are the coordinates of the points $P,R$ and $Q$?

• A. $P(3,2),R(3,0),Q(3,1)$
• B. $P(3,2),R(3,0),Q(3,-1)$
• C. $P(2,2),R(3,1),Q(3,-1)$
• D. $P(3,2),R(1,3),Q(3,0)$

Answer 1

Answer: (B)

$P(3,2),R(3,0),Q(3,-1)$

Any point on a line parallel to the $Y$-axis and at a distance $a$ will have the co-ordinates $P(x,y)=(a,y)$

i.e. $y$ may take any value but $x$ remains constant which is $a$. So the difference between the abscissae of any two points is $a-a=0.$

Here, $a=3$ units.

The ordinate of $P$ is $2⟶$ the co-ordinates are $P(3,2).$

Similarly, The ordinate of $R$ is $0⟶$ the co-ordinates are $R(3,0)$.

And, the ordinate of $Q$ is $-1⟶$ the co-ordinates of $Q$ are $Q(3,-1)$