Question

A line intersects the y-axis and x-axis at P and Q , respectively. If (2,-5) is the mid-point of PQ, then the coordinates of P and Q are, respectively

 

Options

•  (0, -5) and (2, 0)

•  (0, 10) and ( - 4, 0)

• (0, 4) and ( -10, 0 )

• (0, - 0) and (4 , 0)

Answer 1

A line intersects the y axis, then the coordinates of P are (0, y) and x axis then the coordinates are Q(x, 0).
Therefore by section formula, 

\[\left( \frac{x + 0}{2}, \frac{0 + y}{2} \right) = \left( 2, - 5 \right)\]
\[ \Rightarrow \left( \frac{x}{2}, \frac{y}{2} \right) = \left( 2, - 5 \right)\]
\[ \Rightarrow \frac{x}{2} = 2, \frac{y}{2} = - 5\]
\[ \Rightarrow x = 4, y = - 10\]

Hence the coordinates of P are (0, −10) and that of Q are (4, 0).