Line u passes through points (-52, -18) and (-29, 53). line v passes through points (90, 33) and (19, 56). are line u and line v parallel or perpendicular?

(y - yo) = m.(x - xo)

Where (x, y) and (xo, yo) are points of a line and m his slope

If both lines have m equal they are parallels, if they are the opposite inverse they are perpendicular

So, let's see.

line which pass by (-52, -18) and (-29, 53)

(53 - (-18)) = m.(-29 - (-52))

53 + 18 = m.(-29 + 52)

71 = m.(23)

m = 71/23

line which pass by (90, 33) and (19, 56)

(56 - 33) = m.(19 - 90)

23 = m.(-71)

m = -23/71

As we see, 71/23 and -23/71 are opposite inverses of one another, so they are perpendicular lines.

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