Answer:
Midpoint = (3.5, 4.5)
Perpendicular bisector = y = [tex]\frac{7}{9}[/tex] x + [tex]\frac{16}{9}[/tex]
Step-by-step explanation:
[] We can solve this using the midpoint formula:
-> See attached
[] Plug-in our coordinates and solve:
[tex](\frac{7+0}{2} ,\frac{0+9}{2} )=(\frac{7}{2} ,\frac{9}{2} )=(3.5,4.5 )[/tex]
[] Now we will find the slope to solve for the perpendicular bisector.
-> We will use slope-intercept form, see attached
[tex]\frac{9-0}{0-7}=\frac{9}{-7}[/tex]
-> The slopes of two perpendicular lines are negative reciprocals of each other, so [tex]\frac{7}{9}[/tex] will be the slope of or perpendicular bisector
-> Now we can solve for the equation by using y – y1 = m ( x – x1), were y1 and x1 are the coordinates of our midpoint
y - 4.5 = [tex]\frac{7}{9}[/tex] (x-3.5)
y - 4.5 = [tex]\frac{7}{9}[/tex] x-[tex]\frac{49}{18}[/tex]
y = [tex]\frac{7}{9}[/tex] x-[tex]\frac{49}{18}[/tex] + 4.5
y = [tex]\frac{7}{9}[/tex] x + [tex]\frac{16}{9}[/tex]
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
