Theorems

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The Distance Formula

d=\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}

Example: Find the distance between point A(5,-7) and B(-6,-2) and leave your answer in radical form.

Solution: Let A be point 1 and B be point 2. We have x_1\ =5,y_1 = -7, x_2 = -6, y_2 = -2

Substituting we have d=\sqrt{(\ -6 -5)^2 + (-2 - -7)^2} = \sqrt{(\ -11)^2 + (-2 +7)^2} = \sqrt{(\ -11)^2 + (+5)^2} = \sqrt{(\ 121 + 25} = \sqrt{146}

Distance & Midpoint 9-2 ME Worksheet

Sum of the Sides of a Triangle

Thm: The sum of two sides of any triangle must be greater than the third side

Example: Given two sides of a triangle are 8 inches and 11 inches, find all the possible lengths of the third side (also known as S3)

Solution: We know that 8 + 11 must be greater than S_3

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