Question

Write an equation of the perpendicular bisector of {J K} , where J=(-6,3) and( K=(3,3) . Wite the equatians of the lines that form the four slides of the riaht trapezold with"

Answer 1

The equation of the perpendicular bisector of segment JK, where J=(-6,3) and K=(3,3), is x = -1.5.

Step-by-step explanation:

To find the equation of the perpendicular bisector of the segment JK, where J=(-6,3) and K=(3,3), we'll follow these steps:

1. Calculate the midpoint of JK, which will be a point on the perpendicular bisector.
2. Determine the slope of JK, and then find the negative reciprocal of this slope for the slope of the perpendicular bisector.
3. Use the point-slope form to write the equation of the line.

Step 1: The midpoint (M) of JK is the average of the x-coordinates and y-coordinates of J and K respectively. M = ((-6 + 3)/2, (3 + 3)/2) = (-1.5, 3).

Step 2: The slope of JK is (3 - 3) / (3 - (-6)) which is 0. The perpendicular bisector will have an undefined slope since the slope of JK is 0, meaning the bisector is vertical.

Step 3: Since the bisector is vertical, its equation is simply x = -1.5, which is the x-coordinate of the midpoint.

Therefore, the equation of the perpendicular bisector of segment JK is x = -1.5.