The given line segment has a midpoint at (3,1)
what is the equation, in slope-intercept form, of the perpendicular bisector of the given line segment

Step-by-step explanation:

We have been given an image of a line segment and we are asked to find the equation of perpendicular bisector of our given line segment in slope-intercept form.

Since we know that the slope of perpendicular line to a given line is negative reciprocal of the slope of the given line.

Let us find the slope of our given line using slope formula.

, where,

= Difference between two y-coordinates,

= Difference between two x-coordinates of same y-coordinates.

Upon substituting the coordinates of points (2,4) and (4,-2) in slope formula we will get,

Now we will find negative reciprocal of to get the slope of perpendicular line.

Since point (3,1) lies on the perpendicular line, so we will substitute coordinates of point (3,1) in slope-intercept form of equation .

Therefore, the equation of perpendicular line will be and option A is the correct choice.

isaiah walks 3 miles due north, turns and then 5 miles due east. how far is he from his starting point?

a^2 + b^2 = c^2

let c = distance from starting point.

(3)^2 + (5)^2 = c^2

9 + 25 = c^2

34 = c^2

sqrt{34} = sqrt{c^2}

sqrt{34} = c