# What is the perimeter of a triangle with corners at #(3 ,9 )#, #(5 ,7 )#, and #(1 ,4 )#?

Perimeter of the triangle is

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The perimeter of the triangle can be calculated by finding the distance between each pair of points and then summing those distances. Using the distance formula ( \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} ) for each pair of points:

- Distance between (3, 9) and (5, 7) is ( \sqrt{(5 - 3)^2 + (7 - 9)^2} = \sqrt{4 + 4} = \sqrt{8} ).
- Distance between (5, 7) and (1, 4) is ( \sqrt{(1 - 5)^2 + (4 - 7)^2} = \sqrt{16 + 9} = \sqrt{25} = 5 ).
- Distance between (1, 4) and (3, 9) is ( \sqrt{(3 - 1)^2 + (9 - 4)^2} = \sqrt{4 + 25} = \sqrt{29} ).

Summing these distances gives the perimeter of the triangle: ( \sqrt{8} + 5 + \sqrt{29} ).

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When evaluating a one-sided 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 one-sided 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 one-sided 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.

- Circle A has a center at #(1 ,-8 )# and a radius of #3 #. Circle B has a center at #(-2 ,-5 )# and a radius of #2 #. Do the circles overlap? If not, what is the smallest distance between them?
- A triangle has corners at #(9 ,1 )#, #(6 ,7 )#, and #(3 ,8 )#. How far is the triangle's centroid from the origin?
- A line passes through #(4 ,9 )# and #(5 ,6 )#. A second line passes through #(1 ,8 )#. What is one other point that the second line may pass through if it is parallel to the first line?
- Circle A has a center at #(2 ,8 )# and an area of #8 pi#. Circle B has a center at #(3 ,2 )# and an area of #27 pi#. Do the circles overlap?
- A line passes through #(8 ,5 )# and #(6 ,4 )#. A second line passes through #(3 ,5 )#. What is one other point that the second line may pass through if it is parallel to the first line?

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