Is centroid and Circumcentre same?

Mathematics

1 answer:

makvit [3.9K]1 year ago

7 0

No, the centroid and Circumcentre are not same but it is same in equilateral triangle.

The intersection of a triangle's perpendicular bisectors is called the circumcenter.A triangle's circumcenter is a location that is equally spaced from each of its vertices.The centroid of a triangle is the location where its medians connect.

Triangle's centroid is always within it. The centroid of a triangle is its center of gravity in physical terms. If the triangle is evenly distributed around the plane's surface and you want to balance it by supporting it at only one point, you must do it near the center of gravity.Are the circumcenter and centroid at the same location? In the case of an equilateral triangle, they will both be.

Therefore, the centroid and Circumcentre are not same but it is same in equilateral triangle.

To learn more about circumcenter click here:

brainly.com/question/16276899

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Consider the function below. f(x)= x^3 + 2x^2 - x - 2 plot the x and y intercepts of the function

dimulka [17.4K]

In the Figure below is shown the graph of this function. We have the following function:

$f(x)=x^3+2x^2-x-2$

The $y-intercept$ occurs when $x=0$ , so:

$f(0)=(0)^3+2(0)^2-(0)-2=-2$

Therefore, the $y-intercept$ is the given by the point:

$\boxed{(0,-2)}$

From the figure we have three $x-intercepts$ :

$\boxed{P_{1}(-2,0)} \\ \boxed{P_{2}(-1,0)} \\ \boxed{P_{3}(1,0)}$

So, the $x-intercepts$ occur when $y=0$ . Thus, proving this:

$f(x)=x^3+2x^2-x-2 \\ \\ For \ P_{1}:\\ If \ x=-2, \ y=(-2)^3+2(-2)^2-(-2)-2=0 \\ \\ For \ P_{2}:\\ If \ x=-1, \ y=(-1)^3+2(-1)^2-(-1)-2=0 \\ \\ For \ P_{3}:\\ If \ x=1, \ y=(1)^3+2(1)^2-(1)-2=0$