A triangle has corners at #(2 ,9 )#, #(4 ,8 )#, and #(5 ,3 )#. How far is the triangle's centroid from the origin?
Distance from centroid
By signing up, you agree to our Terms of Service and Privacy Policy
The centroid of a triangle is the average of its vertices. The centroid's coordinates are given by the average of the coordinates of the vertices.
The centroid's ( x )-coordinate is ( \frac{2 + 4 + 5}{3} = \frac{11}{3} ). The centroid's ( y )-coordinate is ( \frac{9 + 8 + 3}{3} = \frac{20}{3} ).
Using these coordinates, we can calculate the distance between the centroid and the origin using the distance formula:
[ \text{Distance} = \sqrt{\left(\frac{11}{3}\right)^2 + \left(\frac{20}{3}\right)^2} = \frac{1}{3}\sqrt{401} ].
By signing up, you agree to our Terms of Service and Privacy Policy
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.
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 #(4 ,3 )# and #(2 ,5 )#. A second line passes through #(5 ,6 )#. 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 ,12 )# and an area of #81 pi#. Circle B has a center at #(1 ,3 )# and an area of #16 pi#. Do the circles overlap? If not, what is the shortest distance between them?
- A line passes through #(1 ,5 )# and #(1 ,7 )#. A second line passes through #(3 ,6 )#. What is one other point that the second line may pass through if it is parallel to the first line?
- Point P(−5, 2) is translated using the rule (x+3, y−1). What is the x-coordinate of P' ?
- A line passes through #(6 ,2 )# and #(5 ,3 )#. A second line passes through #(7 ,7 )#. What is one other point that the second line may pass through if it is parallel to the first line?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7