What is the perimeter of a triangle with corners at #(6 ,4 )#, #(9 ,2 )#, and #(5 ,1 )#?
Perimeter of triangle ABC
Using distance formula, let us calculate the lengths of the triangle.
Given A (6,4), B (9,2), C(5,1)
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To find the perimeter of a triangle with corners at the given coordinates, you can calculate the distance between each pair of points and then add up those distances.
Using the distance formula ( d = \sqrt{(x_2  x_1)^2 + (y_2  y_1)^2} ), where ((x_1, y_1)) and ((x_2, y_2)) are the coordinates of two points:

Distance between (6, 4) and (9, 2): [ d_1 = \sqrt{(9  6)^2 + (2  4)^2} = \sqrt{3^2 + (2)^2} = \sqrt{9 + 4} = \sqrt{13} ]

Distance between (9, 2) and (5, 1): [ d_2 = \sqrt{(5  9)^2 + (1  2)^2} = \sqrt{(4)^2 + (1)^2} = \sqrt{16 + 1} = \sqrt{17} ]

Distance between (5, 1) and (6, 4): [ d_3 = \sqrt{(6  5)^2 + (4  1)^2} = \sqrt{1^2 + 3^2} = \sqrt{1 + 9} = \sqrt{10} ]
Now, add up the distances to find the perimeter: [ \text{Perimeter} = d_1 + d_2 + d_3 = \sqrt{13} + \sqrt{17} + \sqrt{10} ] [ \text{Perimeter} \approx 3.61 + 4.12 + 3.16 ] [ \text{Perimeter} \approx 10.89 ]
So, the perimeter of the triangle is approximately 10.9 units.
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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 line passes through #(9 ,5 )# and #(2 ,8 )#. A second line passes through #(7 ,3 )#. What is one other point that the second line may pass through if it is parallel to the first line?
 A triangle has corners at #(3 ,4 )#, #(6 ,7 )#, and #(2 ,8 )#. How far is the triangle's centroid from the origin?
 Circle A has a center at #(6 ,4 )# and a radius of #8 #. Circle B has a center at #(2 ,5 )# and a radius of #5 #. Do the circles overlap? If not, what is the smallest distance between them?
 A triangle has corners at #(4 ,6 )#, #(3 ,9 )#, and #(7 ,2 )#. How far is the triangle's centroid from the origin?
 Circle A has a center at #(1 ,5 )# and an area of #12 pi#. Circle B has a center at #(8 ,1 )# and an area of #3 pi#. Do the circles overlap? If not, what is the shortest distance between them?
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