Centroid Quiz

What is the definition of centroid?

• The centroid is the point where the perpendicular bisectors of a polygon intersect.

• The centroid is the point where the diagonals of a polygon intersect.

• The centroid is the point where all the sides of a polygon intersect.

• The centroid is the geometric center of a plane figure or a three-dimensional object.

Which of the following properties is true for the centroid of a triangle?

• The centroid of a triangle is the point of intersection of the perpendicular bisectors of the sides.

• The centroid of a triangle is always located inside the triangle.

• The centroid of a triangle is equidistant from all three vertices of the triangle.

• The centroid of a triangle divides each median into a 2:1 ratio.

What is the formula to find the centroid of a triangle?

• (x1 + x2 + x3)/2, (y1 + y2 + y3)/2

• (x1 + x2 + x3)/4, (y1 + y2 + y3)/4

• (x1 + x2 + x3)/3, (y1 + y2 + y3)/3

• (x1 + x2 + x3)/5, (y1 + y2 + y3)/5

Which of the following is NOT an application of the centroid?

• Finding the area of a polygon

• Measuring the similarity between two data points

• Determining the average position of a set of data points

• Calculating the center of mass of an object

What is the ratio in which the centroid divides the medians of a triangle?

• 1:2

• 3:1

• 2:1

• 4:1

What is the name of the point where the medians of a triangle intersect?

• centroid

• orthocenter

• incenter

• circumcenter

Which of the following statements is true about the centroid of an equilateral triangle?

• The centroid of an equilateral triangle is located at the midpoint of each side.

• The centroid of an equilateral triangle is two-thirds of the distance from each vertex to the opposite side.

• The centroid of an equilateral triangle is one-third of the distance from each vertex to the opposite side.

• The centroid of an equilateral triangle is located at one of the vertices.

What is the geometric shape formed by connecting the midpoints of the sides of a triangle?

• orthocenter

• centroid

• medial triangle

• incenter

Which of the following is NOT a property of the centroid of a triangle?

• The centroid divides each median into two segments of equal length.

• The centroid is the intersection point of the medians.

• The centroid is always inside the triangle.

• The centroid is always outside the triangle.

What is the formula to find the x-coordinate of the centroid of a triangle?

• (x1 + x2 + x3) / 5

• (x1 + x2 + x3) / 4

• (x1 + x2 + x3) / 3

• (x1 + x2 + x3) / 2