Answer: 5
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One method is to plot the points P(3,6) and Q(7,3) on the same xy grid. Plot a third point R at (3,3). See the diagram below.
A right triangle forms in which we can find the legs PR = 3 and RQ = 4. The hypotenuse is found through the pythagorean theorem.
a^2+b^2=c^2
3^2+4^2 = c^2
9+16 = c^2
c^2 = 25
c = sqrt(25)
c = 5
This is the length of PQ
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Or you can use the distance formula which is effectively using the pythagorean theorem just in a slightly different format (though it may not be obvious).
[tex]d = \text{Distance from P to Q}\\\\d = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\\\\d = \sqrt{(3-7)^2+(6-3)^2}\\\\d = \sqrt{(-4)^2+(3)^2}\\\\d = \sqrt{16+9}\\\\d = \sqrt{25}\\\\d = 5\\\\[/tex]
