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How do you find out if two lines are perpendicular? Check the slopes! Perpendicular lines have negative inverse slopes. In equation form, if you have two lines,

y1 = m1*x + b1, and

y2 = m2*x + b2

Then if they are perpendicular,

m1 = -1/m2

So, you have to calculate the slope of the lines connecting each point. Slope can be calculated as the change in y over the change in x. Mathematically, if you have two points, (x1,y1) and (x2,y2), the slope of the line between them is

m = (y2 - y1)/(x2 - x1)

Let's identify the slope of the line between W and X as m_WX, between X and Y as m_XY, etc. Then

m_WX = (0-4) / (3-0) = -4/3

m_XY = (-3-0) / (-1-3) = -3/-4 = 3/4

m_YZ = (3-(-3)) / (-5.5-(-1)) = 6/-4.5 = -12/9 = -4/3

m_ZW = (4-3) / (0-(-5.5)) = 1/5.5 = 2/11

So, what lines are perpendicular? Which lines satisfy m1 = -1/m2? Looks like WX and XY are the only ones. So there's a right angle at point X.

By the way, what lines are parallel? Parallel lines have the same slope, so WX and YZ are parallel.

One way is to work out the gradients or slopes of all the sides. Remember that:

gradient of AB = gradient of CD if and only if AB is parallel to CD

(gradient of AB) (gradient of CD) = -1 if and only if AB is perpendicular to CD.