Question bank: Analytic Geometry: Centroid

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Question 1:

Medium

Analytic Geometry: Centroid

Question 2:

Medium

In a Cartesian plane, a triangle ABC is located with its vertices at A(4,2), B(-2, -6), and C(6, -4). The centroid of a triangle is the point of intersection of the medians of that triangle, and is represented by the point G. Knowing this, calculate the coordinates of the centroid G of this triangle.

Analytic Geometry: Centroid

Question 3:

Easy

Consider a triangle in the Cartesian plane whose vertices are A(1, 3), B(4, 2), and C(2, 5). Determine the coordinates of the centroid of this triangle, which is the point of intersection of the medians of the triangle. To do this, calculate the midpoint of each side of the triangle, which is the midpoint of the line segment connecting two vertices, and then calculate the arithmetic mean of the coordinates of the midpoints to obtain the coordinates of the centroid. Explain the concept of centroid and its importance in Euclidean geometry.

Analytic Geometry: Centroid

Theorical Question

Contextualized Question

Question 4:

Very Easy

Consider a triangle ABC in the Cartesian plane, where A(3, 4), B(5, 8), and C(7, 2). To calculate the coordinates of the centroid G of this triangle, which is the point of intersection of the medians, we apply the formula (1/3)*(x_A + x_B + x_C, y_A + y_B + y_C). Calculate the coordinates of the centroid G.

Analytic Geometry: Centroid

Multidisciplinary Question

Question 5:

Hard

Consider a triangle ABC in the Cartesian plane, where A = (1, 2), B = (4, 6), and C = (7, 2). Let G be the centroid of this triangle and H be the midpoint of segment AB. Determine the coordinates of G and H and discuss the relationship between vectors AG and BH.

Analytic Geometry: Centroid

Theorical Question

Contextualized Question

IARA TIP

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