What is the perimeter of a triangle with corners at #(3 ,6 )#, #(1 ,5 )#, and #(2 ,1 )#?
The triangle is made up of three line segments. We can determine the length of each side through the distance formula and then add them for the entire perimeter of the triangle.
Thus the perimeter of the triangle is
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To find the perimeter of a triangle with corners at (3, 6), (1, 5), and (2, 1), we use the distance formula to calculate the lengths of each side of the triangle:
The distance formula between two points ((x_1, y_1)) and ((x_2, y_2)) is given by: [ d = \sqrt{(x_2  x_1)^2 + (y_2  y_1)^2} ]

Distance between (3, 6) and (1, 5): [ d_1 = \sqrt{(1  3)^2 + (5  6)^2} = \sqrt{(2)^2 + (1)^2} = \sqrt{4 + 1} = \sqrt{5} ]

Distance between (1, 5) and (2, 1): [ d_2 = \sqrt{(2  1)^2 + (1  5)^2} = \sqrt{1^2 + (4)^2} = \sqrt{1 + 16} = \sqrt{17} ]

Distance between (2, 1) and (3, 6): [ d_3 = \sqrt{(3  2)^2 + (6  1)^2} = \sqrt{1^2 + 5^2} = \sqrt{1 + 25} = \sqrt{26} ]
Finally, we sum up the lengths of the sides to find the perimeter: [ \text{Perimeter} = d_1 + d_2 + d_3 = \sqrt{5} + \sqrt{17} + \sqrt{26} ]
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
 A triangle has corners at #(5 ,2 )#, #(4 ,6 )#, and #(3 ,5 )#. How far is the triangle's centroid from the origin?
 A triangle has corners at #(2 ,9 )#, #(4 ,8 )#, and #(4 ,3 )#. How far is the triangle's centroid from the origin?
 How does one derive the Midpoint Formula?
 Circle A has a center at #(2 ,1 )# and a radius of #3 #. Circle B has a center at #(1 ,3 )# and a radius of #2 #. Do the circles overlap? If not what is the smallest distance between them?
 Circle A has a center at #(5 ,2 )# and a radius of #6 #. Circle B has a center at #(4 ,8 )# and a radius of #5 #. Do the circles overlap? If not, what is the smallest distance between them?
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