Use formulas to complete the following problems and show all calculations.

Question

1. If M is the midpoint of segment AB, find the coordinates of B; given that A = (-8, 9) and M = (-6, 6).

2. Calculate the distance between A and B.

3. Find the equation in point - slope form of the line that is the perpendicular bisector of the segment between (16, -4) and (-2, -76).

4. What is the length of the dashed line? 12mm, 3mm, 84mm

 

I try to solve these problem but its too confusing to understand it. 

Answer 1

1)

 

Use the midpoint formula.

 

M = ( (A_x + B_x) / 2 , (A_y + B_y) )

 

(-6, 6) = ( (-8 + B_x) / 2 , (9 + B_y) / 2 )

 

 

Set these two equations.

 

-6 = (-8 + B_x) / 2                  and                 6 = (9 + B_y) / 2

 

-12 = -8 + B_x                       and                  12 = 9 + B_y

 

 

Then solving the equations for the variables,

 

Point B = (B_x , B_y)

 

 

 

2)

 

Use distance formula.

 

D_AB = √[(A_x - B_x)² + (A_y - B_y)²]

 

 

 

3)

 

This line passes through the midpoint because it is a bisector of the segment formed by those two points.

 

First, find the midpoint between the points using the midpoint formula from problem 1.  I leave that part to you.

 

M = (M_x , M_y)  ----->  coordinate of midpoint

 

 

Find the slope between the points. 

 

m = (-76 - (-4)) / (-2 - 16)

m = -72 / -18

m = 4

 

 

Then the equation of the line in point-slope form is

 

y - M_y = (-1/4)(x - M_x)