Question

Determine if lines passing through the points are Parallel,perpendicular,or neither line 1:(-2,2)and (2,-4) line 2:(3,6) and (5,3)

Answer 1

You can tell if two lines are parallel, perpendicular, or neither by looking at their slopes
`m_1` and
`m_2`:

• If
  `m_1=m_2`, i.e. if the two lines have the same slope, the lines are parallel
• If
  `m_1\cdot m_2=-1`, the lines are perpendicular
• In all other cases, the lines are not parallel nor perpendicular.

Given two points
`A = (x_A,y_A),\ B = (x_B,y_B)` of a line, the slope is defined as the ratio between the y and x variation:

`m = (\Delta y)/(\Delta x) = (y_B-y_A)/(x_B-x_A)`

So in this case, we have

`m_1 = (2-(-4))/(-2-2) = (6)/(-4) = -(3)/(2)`

`m_2 = (3-6)/(5-3) = (-3)/(2) = -(3)/(2)`

Since the two slopes are the same, the two lines are parallel.