Question

Can I have help with the question

Answer 1

Midpoint = (3.5, 4.5)

Perpendicular bisector = y =
`(7)/(9)` x +
`(16)/(9)`

Explanation:

[] We can solve this using the midpoint formula:

-> See attached

[] Plug-in our coordinates and solve:

`((7+0)/(2) ,(0+9)/(2) )=((7)/(2) ,(9)/(2) )=(3.5,4.5 )`

[] Now we will find the slope to solve for the perpendicular bisector.

-> We will use slope-intercept form, see attached

`(9-0)/(0-7)=(9)/(-7)`

-> The slopes of two perpendicular lines are negative reciprocals of each other, so
`(7)/(9)` 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 =
`(7)/(9)` (x-3.5)

y - 4.5 =
`(7)/(9)` x-
`(49)/(18)`

y =
`(7)/(9)` x-
`(49)/(18)` + 4.5

y =
`(7)/(9)` x +
`(16)/(9)`

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