Answer:
14. 
15. 
16. 
17. 
18. 
19. 
20. 
Step-by-step explanation:
Solving (14):
Given


Equation in
form is:

Substitute values for y1, m and x1



Collect Like Terms


Solving (15):
Given


Equation in
form is:

Substitute values for y1, m and x1



Collect Like Terms


Solving (16):
Given


First, we need to calculate the 





Equation in
form is:

Substitute values for y1, m and x1



Collect Like Terms


Solving (17):
Given


First, we need to calculate the 





Equation in
form is:

Substitute values for y1, m and x1



Collect Like Terms


18.
Given


Since the given point is parallel to the line equation, then the slope of the point is calculated as:

Where
represents the slope
Going by the format of an equation,
; by comparison

and

Equation in
is:

Substitute values for y1, m and x1





19.
Given


Since the given point is parallel to the line equation, then the slope of the point is calculated as:

Where
represents the slope
Going by the format of an equation,
; by comparison

and




Equation in
is:


Substitute values for y1, m and x1



Collect Like Terms


20.
Given


First, we need to calculate the slope of the given points





Next, we determine the slope of the perpendicular bisector using:



Next, is to determine the coordinates of the bisector.
To bisect means to divide into equal parts.
So the coordinates of the bisector is the midpoint of the given points;
![Midpoint = [\frac{1}{2}(x_1+x_2),\frac{1}{2}(y_1+y_2)]](https://tex.z-dn.net/?f=Midpoint%20%3D%20%5B%5Cfrac%7B1%7D%7B2%7D%28x_1%2Bx_2%29%2C%5Cfrac%7B1%7D%7B2%7D%28y_1%2By_2%29%5D)
![Midpoint = [\frac{1}{2}(-10+2),\frac{1}{2}(3+7)]](https://tex.z-dn.net/?f=Midpoint%20%3D%20%5B%5Cfrac%7B1%7D%7B2%7D%28-10%2B2%29%2C%5Cfrac%7B1%7D%7B2%7D%283%2B7%29%5D)
![Midpoint = [\frac{1}{2}(-8),\frac{1}{2}(10)]](https://tex.z-dn.net/?f=Midpoint%20%3D%20%5B%5Cfrac%7B1%7D%7B2%7D%28-8%29%2C%5Cfrac%7B1%7D%7B2%7D%2810%29%5D)

So, the coordinates of the midpoint is:

Equation in
form is:

Substitute values for y1, m and x1:
& 



Collect Like Terms

