Question

The coordinates of the point P are (-3, 2). Find the coordinates of the point Q which lies on the line joining P and origin such that OP = OQ.

Answer 1

Hint: In this question line formed by two points P and Q and OP = OQ is given. So to find out the coordinate of Q, we will apply the mid-point theorem which states that the x coordinate is the average of the x coordinates of the end points and y coordinate is the average of the y coordinates of the endpoints.

Complete step-by-step answer:

Given the point P = (-3, 2)
Point O = (0, 0)
Let point Q = (x, y)
The point Q which lies on the line joining P and origin such that OP = OQ
i.e. O is the midpoint of PQ
We know that if line AB has coordinates as $A({x_1},{y_1})$ and $B({x_2},{y_2})$ then its middle coordinate can be expressed as $\left( {\dfrac{{{x_1} + {x_2}}}{2},\dfrac{{{y_1} + {y_2}}}{2}} \right)$ this is called mid-point theorem.
So, by applying the mid-point theorem, we have
$
  \dfrac{{x + \left( { - 3} \right)}}{2} = 0{\text{ and }}\dfrac{{y + 2}}{2} = 0 \\
  x = 3{\text{ and y}} = - 2 \\
$
 Hence the coordinate of $Q(3, - 2)$.

Note: In order to solve these types of questions related to the mid-point theorem, understand the concept of this theorem first. In coordinate geometry there are many formulas to learn. So it is best to understand the concept using diagrams and also draw diagrams during solving these types of questions.