Understanding the Centroid of a Triangle

This video tutorial explains how to find the centroid of a triangle. It begins by plotting points on a Cartesian plane to form a triangle. The concept of medians is introduced, showing how they intersect at the centroid. The video details the process of finding midpoints of line segments and constructing medians. It then demonstrates solving for the centroid using linear equations. The tutorial concludes with a verification of the centroid and encourages the use of graphing tools for visualization.

What is the centroid of a triangle?

• The point where the angle bisectors meet

• The point where the medians intersect

• The point where the altitudes intersect

• The point where the perpendicular bisectors meet

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CCSS.HSG.GPE.B.6

How do you find the midpoint of a line segment?

• By subtracting the x-coordinates and y-coordinates of the endpoints

• By averaging the x-coordinates and y-coordinates of the endpoints

• By multiplying the x-coordinates and y-coordinates of the endpoints

• By dividing the x-coordinates and y-coordinates of the endpoints

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CCSS.HSG.CO.C.10

What is the purpose of constructing medians in a triangle?

• To locate the centroid

• To determine the type of triangle

• To find the area of the triangle

• To calculate the perimeter

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CCSS.HSG.GPE.B.7

How can you find the centroid using a linear system?

• By finding the intersection of angle bisectors

• By calculating the average of all vertices

• By using the Pythagorean theorem

• By solving for the intersection of two medians

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CCSS.8.EE.B.5

What is the slope of a line if the rise is -3 and the run is 5/2?

• -6/5

• 5/6

• -5/6

• 3/5

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CCSS.8.EE.B.5

Which tool is recommended for visualizing the centroid?

• AutoCAD

• Google Sheets

• Desmos

• Microsoft Excel

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CCSS.8.EE.C.7B

What is the benefit of using graphing tools like Desmos?

• They provide exact numerical solutions

• They eliminate the need for understanding concepts

• They help visualize the problem

• They are faster than manual calculations

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CCSS.8.EE.B.6

CCSS.8.F.A.3

What is the y-intercept of the line with the equation y = -6/5x + 8/5?

• -8/5

• -6/5

• 8/5

• 6/5

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CCSS.HSG.C.A.3

What is the x-coordinate of the centroid found in the video?

• 2/3

• -1/3

• 1/3

• -2/3

What is the final step in finding the centroid using equations?

• Graphing the equations

• Substituting the x-value into one of the equations

• Finding the slope of the lines

• Calculating the area of the triangle