Straight Line Question 298

Question: A line meets x?axis and y-axis at the points A and B respectively. If the middle point of AB be $ (x_1,\ y_1), $ then the equation of the line is

Options:

A) $ y_1x+x_1y=2x_1y_1 $

B) $ x_1x+y_1y=2x_1y_1 $

C) $ y_1x+x_1y=x_1y_1 $

D) $ x_1x+y_1y=x_1y_1 $

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Answer:

Correct Answer: A

Solution:

  • Obviously, $ x_1=\frac{a}{2} $ and $ y_1=\frac{b}{2} $ .Therefore the equation of line $ AB $ is $ \frac{x}{a}+\frac{y}{b}=1 $
    Þ $ \frac{x}{2x_1}+\frac{y}{2y_1}=1\Rightarrow xy_1+yx_1=2x_1y_1 $ .