given the points A(-2,5) and B(4,3) write the l equation of the line that is perpendicular bisector of AB

Answer 1

What you need to do first is to get the midpoint and slope of the line segment.

A(-2,5) and B(4,3)

The midpoint formula is:

x=(x₁+x₂)/2, y=(y₁+y₂)/2

x=(-2+4)/2 = 1

y=(5+3)/2 = 4

The midpoint is at (1,4).

Next, the slope (m).

m=(y₂ - y₁)/(x₂ - x₁)

m=(3-5)/(4+2) = -2/6 = -1/3

A perpendicular bisector passes through the midpoint and form a right angle. Two lines form a right angle when their slopes are negative reciprocals:

Calculated m =-1/3

Negative reciprocal of m = 3

Let's use the point slope form of linear equation:

y - y₁ = m (x - x₁)

Therefore, the equation (l) is:

y - 4 = 3(x - 1)