Question

Please help with this question!!

Answer 1

`y +3 = -(1)/(2)  (x +3)`

Explanation:

Point-slope has the form
`y -y_(1) = m (x -x_(1) )` where

• (x,y) are the input and output values for the function
• 
  `(x_(1) ,y_(1)) is a coordinate point on the line`
• m is the slope or rate of change of the line

We find m by subtracting the two points.

`m=(y_(2) -y_(1) )/(x_(2)-x_(1)  )`

You can choose the order. Lets start with B followed by C.

`m=(1 -(-7))/((-1)-(-5))=(1+7)/(-1+5) =(8)/(4) =2`

However, we are finding the perpendicular bisector to this line. Perpendicular lines have a unique relationship between slopes, specifically that they are the negative reciprocal. For m=2, the slope of the bisector will be m=
`-(1)/(2)`. Neither B or C are on the bisector line as they are the endpoint of the original line. If we find the midpoint between them, we will find the starting point of the perpendicular bisector.

To find the midpoint, we take the average between the two points or
`((x_(1)+x_(2))/(2) ), ((y_(1)+y_(2))/(2))`.

We substitute B and C.

`((x_(1)+x_(2))/(2) ), ((y_(1)+y_(2))/(2)) \\((-1+-5)/(2) ), ((1+-7)/(2)) \\((-6)/(2) ), ((-6)/(2)) \\(-3,-3)`.

We take out slope m=
`-(1)/(2)` and our midpoint (-3,-3) into the point-slope formula.

`y -(-3) = -(1)/(2)  (x -(-3) )\\y +3 = -(1)/(2)  (x +3)`