Theorems

(Difference between revisions)

Revision as of 22:58, 18 October 2009

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

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

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 $S 3$ )

Solution: Since we know that 8 + 11 must be greater than $S 3$ , we have $8\ + 11 > S_3$ so $S_3\ <19$

@@ Line 21: / Line 21: @@
 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 <math>S_3</math>)
-Solution: We know that 8 + 11 must be greater than S_3
+Solution: Since we know that 8 + 11 must be greater than <math>S_3</math>, we have <math>8\ + 11 > S_3</math>
+so <math>S_3\ <19 </math>
 [[Category:Geometry]]