Question
What is the equation of the line through $$\left( {1,\,2} \right)$$ so that the segment of the line intercepted between the axes is bisected at this point ?
A.
$$2x - y = 4$$
B.
$$2x - y + 4 = 0$$
C.
$$2x + y = 4$$
D.
$$2x + y + 4 = 0$$
Answer :
$$2x + y = 4$$
Solution :
$$\eqalign{ & \frac{{0 + x}}{2} = 1\,\,;\,\,\frac{{0 + y}}{2} = 2 \cr & x = 2\,\,;\,\,y = 4 \cr} $$
Equation of line passing through $$\left( {2,\,0} \right)$$ and $$\left( {0,\,4} \right)$$
$$\eqalign{ & y - 0 = \frac{{4 - 0}}{{0 - 2}}\left( {x - 2} \right) \cr & {\text{or }}y = - 2x + 4 \cr & {\text{or }}2x + y = 4 \cr} $$
$$\eqalign{ & \frac{{0 + x}}{2} = 1\,\,;\,\,\frac{{0 + y}}{2} = 2 \cr & x = 2\,\,;\,\,y = 4 \cr} $$
Equation of line passing through $$\left( {2,\,0} \right)$$ and $$\left( {0,\,4} \right)$$
$$\eqalign{ & y - 0 = \frac{{4 - 0}}{{0 - 2}}\left( {x - 2} \right) \cr & {\text{or }}y = - 2x + 4 \cr & {\text{or }}2x + y = 4 \cr} $$