question_answer

ABCD is a parallelogram. Co-ordinates of A, B and C are (5, 0), (-2, 3) and (-1, 4) respectively. What will be the equation of line AD?

A) \[y=2x-5\]

B) \[y=x+5\]

C) \[y=2x+5\]

D) \[y=x-5\]

Correct Answer: D

Solution :

Co-ordinates of point O \[=\left( \frac{5-1}{2}.\frac{4+0}{2} \right)=(2,2)\]             If the co-ordinates of pint D be \[(x,y),\]then \[\frac{x-2}{2}=2\Rightarrow x=4+2=6\]and \[\frac{y+3}{2}=2\Rightarrow y=4-3=1\] \[\therefore \]Equation of a straight line passing through \[({{x}_{1}},{{y}_{1}})\] and \[({{x}_{2}},{{y}_{2}})\]is: \[y-{{y}_{1}}=\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}(x-{{x}_{1}})\] \[(({{x}_{1}},{{y}_{1}})=5,0,({{x}_{2}},{{y}_{2}})=6,1)\] \[\Rightarrow y-0=\frac{1-0}{6-5}(x-5)\] \[\Rightarrow y=x-5\]