# What is the perimeter of a triangle with corners at #(6 ,4 )#, #(9 ,2 )#, and #(5 ,7 )#?

Each side of the triangle can be measured by the distance formula:

Let's use labels for corners:

Then

Then the perimeter of the given triangle is:

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To find the perimeter of the triangle with corners at (6, 4), (9, 2), and (5, 7), you need to calculate the distances between these points and then sum them up. You can use the distance formula, which states that the distance between two points (x₁, y₁) and (x₂, y₂) in a plane is given by:

[ \text{Distance} = \sqrt{(x₂ - x₁)^2 + (y₂ - y₁)^2} ]

Apply this formula to find the lengths of the sides of the triangle, then add them together to find the perimeter.

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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.

- A line passes through #(2 ,8 )# and #( 1, 5 )#. A second line passes through #( 6, 8 )#. What is one other point that the second line may pass through if it is parallel to the first line?
- How do we find out whether four points #A(3,-1,-1),B(-2,1,2)#, #C(8,-3,0)# and #D(0,2,-1)# lie in the same plane or not?
- A triangle has corners at #(5 ,1 )#, #(7 ,2 )#, and #(6 ,7 )#. How far is the triangle's centroid from the origin?
- What is the perimeter of a triangle with corners at #(3 ,6 )#, #(1 ,5 )#, and #(2 ,1 )#?
- Circle A has a center at #(8 ,-1 )# and a radius of #3 #. Circle B has a center at #(-2 ,-2 )# and a radius of #7 #. Do the circles overlap? If not, what is the smallest distance between them?

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