Points and Slopes

Question

Given the points A(-1, 6) and B(2, -3), what is?:
a) The slope of AB
b) Length of AB
c) The co-ordinates of the midpoint of AB
d) The equation of a line perpendicular to AB that passes through the point (4, 7). Leave your answer in standard form

Answer 1

a)

 

Use the slope formula.  I trust that you know this formula.

 

 

b)

 

Use the distance formula.

 

d = √[(A_x - B_x)² + (A_y - B_y)²]

 

 

c)

 

Use the midpoint formula

 

(M_x , M_y) = (  (A_x + B_x) / 2  ,    (A_y + B_y) / 2 )

 

 

The idea of midpoint is to take the average between two x coordinates, giving you M_x, and average between two y-coordinate, giving you M_y.

 

 

d)

 

Use the point-slope form of the line.  Since you want perpendicular line, the slope of this line must be the negative reciprocal of the original line.

 

The standard form of the line using point-slope form is

 

-mx + y = -mx₁ + y₁