Find the equation of the line passing through the midpoint of the points A(2,7) and B(5,11) perpendicular to the line segment AB.

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efterynzl · Accepted Answer

The midpoint of the points A(2,7) and B(5,11) is given by:  (                    x        1            +              x        2              2    ,                    y        1            +              y        2              2    )  =  (            2      +      5        2    ,            7      +      11        2    )    =  (      7    2    ,      18    2    )  =  (      7    2    ,  9  )The gradiant of the perpendicular lin would be equal to the negative recciprocal of the gradient of the original line.Gradient of original line:      Change in y    change in x      =            11      −      7              5      −      2        =      4    3  Gradient of perpendicular line   =  −      3    4  We can find the equation of a line if we have x and y cooedinate and the gradient through the equation:  y  −      y    1    =  m  (  x  −      x    1    )substitute       y    1   for the midpoint y coordinate       x    1   for the midpoint x coordinate, for the gradient of the perpendicular line  y  −  9  =  −      3    4    (  x  −      7    2    )    y  =  −            3      x        4    +      21    8    +  9    y  =  −            3      x        4    +      93    8  Hence,The equation of the line which is passing through the midpoint of the points A(2,7) and B(5,11) perpendicular to the line segment AB is  y  =  −            3      x        4    +      93    8

Find the equation of the line passing through the midpoint of the points A(2,7) and B(5,11) perpendicular to the line segment AB.

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