Use the information to answer the question.

Information
A coordinate plane.Short description, A coordinate plane.,Long description,
Line A B and point P are on the coordinate plane. Line A B has A at the point (negative 4 comma 2) and B at the point (2 comma negative 2). Point P is not on the line and is at the point (1 comma 2).

Question
What is the equation of the line perpendicular to line A B that passes through point P?

Answer options with 4 options
A.
y equals 3-halves x plus 1-half

B.
y equals negative 2-thirds x minus 2-thirds

C.
y equals 2-thirds x plus 14-thirds

D.
y equals negative 3-halves x minus 4

1 answer

The slope of line AB can be calculated as (2 - (-2)) / (-4 - 2) = 4 / -6 = -2/3.

Since the line perpendicular to AB will have a slope that is the negative reciprocal of -2/3, it will have a slope of 3/2.

Using point-slope form, the equation of the line passing through point P (1, 2) with a slope of 3/2 is:
y - 2 = 3/2(x - 1)
y - 2 = 3/2x - 3/2
y = 3/2x - 3/2 + 2
y = 3/2x + 1/2

So, the equation of the line perpendicular to AB that passes through point P is:
A. y = 3/2x + 1/2