Question bank: Analytic Geometry: Centroid

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Question 1:

Very Easy

The centroid of triangle ABC with vertices A(0,0), B(5,1), and C(1,2) is:

Analytic Geometry: Centroid

Basic Calculus

Question 2:

Hard

Consider a triangle ABC in the Cartesian plane, where A = (2,3), B = (4,1), and C = (6,5). An Architecture student is designing a new building and wants to position a support pillar at the centroid of the triangle, which is the point of intersection of the medians. A sensor spring will be installed at the top of the pillar to measure the force exerted by the structure. The force measured by the spring is directly proportional to the sum of the squares of the distances from the pillar to the vertices. Calculate the coordinates of the centroid of the triangle and then calculate the sum of the squares of the distances from the centroid to the vertices of the triangle. Based on this information, explain how the centroid can be a strategic location for the installation of the pillar, considering the principles of balance and force distribution in architectural structures.

Analytic Geometry: Centroid

Multidisciplinary Question

Question 3:

Easy

In a Biology class, students are working on a problem that involves analyzing the populations of different plant species in an ecosystem. To better understand the spatial distribution of these plants, it is necessary to calculate the centroid of a triangle formed by three sampling points. The points A(2, 4), B(6, 1), and C(4, 6) represent the positions of the samples on the Cartesian plane, where the x and y coordinates are measured in meters. Based on these points, determine the centroid of the formed triangle and explain in terms of Biology the relevance of the centroid for studying the distribution of plant populations in the ecosystem.

Analytic Geometry: Centroid

Multidisciplinary 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:

Medium

Consider a triangle ABC in the Cartesian plane, whose vertices are given by the coordinates A(-2,3), B(4, -1) and C(1, 2). The Centroid is the point where the medians of a triangle intersect, being considered the center of mass of the system. Knowing this, calculate the coordinates of the centroid of this triangle.

Analytic Geometry: Centroid

IARA TIP

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