Chapter 6 tesdt

Front

What is the formula to find the centroid of a triangle with vertices (x1, y1), (x2, y2), (x3, y3)?

Back

The centroid (G) is given by G = ((x1 + x2 + x3)/3, (y1 + y2 + y3)/3).

Front

If the distance between two bases on a baseball field is 90 feet, what is the distance from first base to second base?

Back

The distance from first base to second base is 90 feet.

Front

What is the perimeter of a triangle if the lengths of its sides are given as AB = 3.4, BC = 4.2, and AC = 3.8?

Back

The perimeter of the triangle is 22.8.

Front

How do you find the value of x if BD = 4x + 5 and BF = 9x, given that D is the centroid?

Back

Set 4x + 5 = 9x and solve for x. The value of x is 2.5.

Front

What is the distance between the shortstop and the pitcher if the second baseman is halfway between first and second base, and the pitcher is halfway between first and third base?

Back

The distance between the shortstop and the pitcher is 45 feet.

Front

Define a centroid in the context of a triangle.

Back

The centroid is the point where the three medians of the triangle intersect, and it is also the center of mass of the triangle.

Front

What is the significance of midpoints in geometry?

Back

Midpoints are used to find the center of a line segment and are essential in constructing medians and centroids in triangles.

Front

How do you calculate the distance between two points (x1, y1) and (x2, y2)?

Back

The distance is calculated using the formula: d = √((x2 - x1)² + (y2 - y1)²).

Front

What is the relationship between the sides of a triangle and its perimeter?

Back

The perimeter of a triangle is the sum of the lengths of all its sides.

Front

Explain the concept of a median in a triangle.

Back

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