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Answer:
Step-by-step explanation:
First, let us find the gradient of AB:
Gradient of AB =
=
We also need to know that The <em>product of gradients which are perpendicular to each other is -1</em>. Using this idea, we can find the gradient of the perpendicular bisector:
(Gradient of perpendicular bisector)( ) = -1
Gradient of perpendicular bisector =
Now, we need to know at which coordinates the perpendicular bisector intersects AB. <em>A perpendicular bisector bisects a line to two equal parts</em>. Hence the <em>coordinates of the intersection point is the midpoint of AB</em>. Thus,
Coordinates of intersection = ( ,
)
= ( 2, 1 )
Now, we can construct our equation. The equation of a line can be formed using the formula where
is the gradient and the line passes through
. Hence by substituting the values, we get:
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