Question

Name the line which have the following characteristics:
1) Passes through (2,3) & (0,-9)
2) Perpendiculat to the line 4x-2x=7 and through (1,-3)
3) Perpendicular to the segments with endpoints (2,1) & (-4,-1) and through the midpoint of the segment.

If possible show some quick work (not the full process)
thank you!!

Answer 1

1. slope = (3+9)/2-0) = 6
so (y-3)/(x-2)=6
cross-multiply, rearrange for a suitable version of the equation

2. slope of give line = 2, so slope of new line is -1/2
then (y+3)/(x-1) = -1/2
cross-multiply, rearrange for a suitable version of the equation

3. midpoint of segment = ((2-4)/2,(1-1)/2) = (-1,0)
slope of given segment = 1/3
so slope of new line = -3
so (y-0)/(x+1) = -3
cross-multiply, rearrange for a suitable version of the equation