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# Find the length and width of the rectangle whose vertices are given.V(-1, -2), W(3, -6), X(9, 0), Y(5, 4)

Find the length and width of the rectangle whose vertices are given.

V(-1, -2), W(3, -6), X(9, 0), Y(5, 4)

To be honest, I'm very visual and like to start things this way whenever possible.  So I plotted the vertices on a grid (graph paper or white paper with tick marks) and we see that the rectangle is titled on an angle.  This is just to get a feel for the problem and I recommend it.

The solution actually requires no plotting.  There are only 4 possible combinations of vertices and since we know its a rectangle, both sets of 2 lines will be parallel, so whatever you choose to solve, you'll get either length or width and the other two will simply be checks on the first.

Lets take side VY:  Since the side is tilted, it will be the hypotenuse of a right triangle with sides x and y.  This method is to use the Pythagorean theorem:

x^2 + y^2 = side^2

Remember vertices are Vertices(x val, y val)

Y(5,4) - V(-1,-2):  x val = 5 -(-1) = 6 and y val =4-(-2)=6.   Since both sides of the triangle are the same, it is a 45,45,90 triangle and the sides are always x, x, x sqrt(2).  So the side VY = 6 sqrt(2) or 6*1.414 = ANSWER: LENGTH:  6 sqrt(2) = approx 8.49.

Now side YX  (hint: it doesnt matter which vertices is first.  if you get negative values, its just a backwards triangle! treat all length values as positive (but respect the vertices + and - values).

Y(5,4) - X(9,0):  x val = 5-9 = -4.  y val=4-0=4.  Since the sides of the triangle are 4 and -4, its also a 45,45,90 (degree angle) triangle.  The hypotenuse or side YX = 4 sqrt(2) = 4*1.414 = approx 5.66

ANSWER: WIDTH: 4 sqrt(2) = approx 5.66