To find this answer, first we must find the slope of the current segment. If the two are perpendicular, the lines will have opposite and reciprocal slopes. To find the slope, use the slope formula.
m = y1 - y2/x1 - x2 m = 9 - 3/6 - 0 m = 6/6 m = 1
Since the slope of the new line will be opposite and reciprocal, the new slope will be -1. Now we can use that along with a point to find the line. Since it is a bisector of the original segment, we know it must go through the midpoint. To find the midpoint, take the average of the x values and the average of the y values. The average of the x's (0 and 6) will give you 3. The average of the y's (3 and 9) will give you 6.
Knowing the slope of -1 and the point (3, 6) we can solve for the y intercept using slope intercept form.
y = mx + b ---> plug in known values 6 = -1(3) + b ----> multiply 6 = -3 + b ---> add 3 to both sides 9 = b
With that and the slope, you can give the equation above.
