question_answer

A line intersects the y ? axis and x ? axis at the points P and Q respectively. If (\[2,\text{ }\text{ }5\]) is the mid-point of PQ, then find the co-ordinates of P and Q.

Answer:

Let co-ordinate of P (0, y)

Co-ordinate of Q (x, 0)

Mid-point is (\[2,\text{ }\text{ }5\])

\[\left( \frac{{{x}_{1}}+{{x}_{2}}}{2},\frac{{{y}_{1}}+{{y}_{2}}}{2} \right)=(2,-5)\]

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

\[\Rightarrow \]                           \[\frac{x}{2}=2;\]                      \[\frac{y}{2}=-5\]

\[\Rightarrow \]                               \[x=4;\]         \[y=-10\]

Co-ordinate of \[P\text{(}0,10)\]

Co-ordinate of \[Q(4,\text{ }0)\]