Question

6) A line perpendicular to the line segment joining the points A(1,0) and B(2,3), divides it at C in the
ratio of 1: 3. Then the equation of the line is
2x + 6y - 9=0
2x + 6y – 7 = 0
2x – 67 – 9 = 0
2x – 6y + 7 = 0​

Answer 1

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

The slope of the given line is m=3−1

Therefore, the slope of any line parallel to the given line is also  m=3−1

The slope intercept form of any parallel line is y=3−1x+c  where c is the y-intercept.

Thus, the x-intercept is (3c,0) and the y-intercept is (0,c).

The distance between the intercepts is to be 10 units, therefore, using the distance formula 

10=(3c)2+c2

100=9c2+c2

c=±10

There are two lines parallel to the given line, such that the distance between the x and y intercepts is 10 units , their equations are:

 y=3−1x+10

And 

y=3−1x−10