Question

Find the equation of the right bisector of the line segment joining the points (3,4) and (-1,2)​

Answer 1

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Answer 2

Given:-

• The right bisector of the line segment.
• The point (3, 4) and (-1, 2)

To find:-

• Find the equation..?

Solutions:-

• The right bisector of a line segment bisects the line segment at 90°

• The end - point of the line segment are given as A (3, 4) and B (-1, 2).

Accordingly,

• Mid - point of AB

=> AB = (3 - 1 /2, 4 + 2 /2)

=> AB = (1, 3)

Therefore,

Slope of the line perpendicular to AB = -1/(1/2) = -2

The equation of the line passing through (1, 3) and having a slope of -2 is.

=> (y - 3) = -2(x - 1)

=> y - 3 = -2x + 2

=> 2x + y = 5

Hence, the required equation of the line is 2x + y = 5.