5.4 Centroid Do Now

Front

What is a centroid in a triangle?

Back

The centroid is the point where the three medians of a triangle intersect. It is also the center of mass of the triangle.

Front

How do you find the centroid of a triangle given its vertices?

Back

The centroid (G) can be found using the formula: G = ((x1 + x2 + x3)/3, (y1 + y2 + y3)/3) where (x1, y1), (x2, y2), and (x3, y3) are the coordinates of the vertices.

Front

What is the relationship between the centroid and the lengths of the segments created by the centroid on the medians?

Back

The centroid divides each median into two segments, with the segment connecting the vertex to the centroid being twice as long as the segment connecting the centroid to the midpoint of the opposite side.

Front

If Z is the centroid of triangle TUV, what is the length of ZV if ZU = 50 and ZY = 30?

Back

ZV = 48, since the centroid divides the median in a 2:1 ratio.

Front

In triangle RST, if X is the centroid and SX = 12, what is the length of RX?

Back

RX = 6, as the centroid divides the median in a 2:1 ratio.

Front

What is the formula for the area of a triangle?

Back

Area = 1/2 * base * height.

Front

How does the centroid affect the balance of a triangle?

Back

The centroid is the balance point of the triangle; if the triangle were made of a uniform material, it would balance perfectly at the centroid.

Front

What is the significance of the centroid in real-world applications?

Back

The centroid is used in various fields such as engineering, architecture, and physics to determine the center of mass and balance of structures.

Front

If the lengths of the medians of a triangle are known, how can you find the centroid?

Back

The centroid can be found by calculating the average of the coordinates of the triangle's vertices, which can be derived from the lengths of the medians.

Front

What is the median of a triangle?

Back

A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side.