Question

if the mid points of the line segment PQ is (-1/2,-1/2),then the coordinates of P and Q is
a) (-1,0) and (0,-1)
b) (1,0) and (0,1)
c) (1,1) and (0,0)
d) (-1,-1) and (0,0)

Answer 1

Answer:

option a.

Step-by-step explanation:

Answer 2

Answer:

The coordinates of P and Q are either (-1,0) & (0,-1) or (-1,-1) & (0,0)

Step-by-step explanation:

Given the mid points of the line segment PQ is $\big(\frac{-1}{2}, \frac{-1}{2}\big)$

Mid points of a line segment of P$({x_{1} , y_{1} }})$ and Q$({x_{2} , y_{2} )$ are given by

                     $\big(\frac{x_{1} +x_{2}}{2}, \frac{y_{1} +y_{2}}{2}\big)$

Equating to the given midpoint,

                      $\big(\frac{x_{1} +x_{2}}{2}, \frac{y_{1} +y_{2}}{2}\big)=\big(\frac{-1}{2}, \frac{-1}{2}\big)$

              $\implies \frac{x_{1} +x_{2}}{2} = \frac{-1}{2}$   and   $\frac{y_{1} +y_{2}}{2}=\frac{-1}{2}$

            $\implies {x_{1} +x_{2}} = {-1}$   and   ${y_{1} +y_{2}}={-1}$

From the given options,

          a) (-1,0) and (0,-1) and d) (-1,-1) and (0,0)

both satisfy the equations, ${x_{1} +x_{2}} = {-1}$ and   ${y_{1} +y_{2}}={-1}$

Therefore, the coordinates of P and Q are either (-1,0) and (0,-1) or (-1,-1) and (0,0)

Hence, the correct answers are options a) and d)