Answer:
Part 1) 
Part 2) 
Part 3)
Part 4) 
Part 5) 
Part 6) 
Part 7) 
Part 8)
case A) The equation of the diagonal AC is 
case B) The equation of the diagonal BD is 
Step-by-step explanation:
Part 1)
step 1
Find the midpoint
The formula to calculate the midpoint between two points is equal to

substitute the values


step 2
The equation of the line into point slope form is equal to

step 3
Convert to standard form
Remember that the equation of the line into standard form is equal to

where
A is a positive integer, and B, and C are integers

Multiply by 7 both sides


Part 2)
step 1
Find the midpoint
The formula to calculate the midpoint between two points is equal to

substitute the values


step 2
Find the slope
The slope between two points is equal to

step 3
we know that
If two lines are perpendicular, then the product of their slopes is equal to -1
Find the slope of the line perpendicular to the segment joining the given points


therefore

step 4
The equation of the line into point slope form is equal to

we have
and point 

step 5
Convert to standard form
Remember that the equation of the line into standard form is equal to

where
A is a positive integer, and B, and C are integers


Part 3)
In this problem AB and BC are the legs of the right triangle (plot the figure)
step 1
Find the midpoint AB


step 2
Find the midpoint BC


step 3
Find the slope M1M2
The slope between two points is equal to

step 4
The equation of the line into point slope form is equal to

we have
and point 

step 5
Convert to standard form
Remember that the equation of the line into standard form is equal to

where
A is a positive integer, and B, and C are integers

Multiply by 8 both sides
Part 4)
In this problem the hypotenuse is AC (plot the figure)
step 1
Find the slope AC
The slope between two points is equal to

step 2
The equation of the line into point slope form is equal to

we have
and point 



step 3
Convert to standard form
Remember that the equation of the line into standard form is equal to

where
A is a positive integer, and B, and C are integers

Multiply by 8 both sides


Part 5)
The longer diagonal is the segment BD (plot the figure)
step 1
Find the slope BD
The slope between two points is equal to
step 2
The equation of the line into point slope form is equal to

we have
and point 



step 3
Convert to standard form
Remember that the equation of the line into standard form is equal to

where
A is a positive integer, and B, and C are integers

Multiply by 4 both sides


Note The complete answers in the attached file