Answered: The three points A = (1, 3), B = (3, 1)…

Elementary Geometry for College Students

6th Edition

ISBN:9781285195698

Author:Daniel C. Alexander, Geralyn M. Koeberlein

Publisher:Daniel C. Alexander, Geralyn M. Koeberlein

Chapter10: Analytic Geometry

Section10.CT: Test

Problem 22CT

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Question

The three points A = (1, 3), B = (3, 1) and C = (−2, −2) are taken as the vertices of a
triangle T.

(a) Determine the midpoints X, Y and Z of the sides BC, AC and AB respectively of
the triangle T.
(b) Find the equations of the three lines AX, BY and CZ.
These lines are called the medians of T.
(c) Show that there is a unique point P which lies on all three of the medians of T.

The point P is called the centroid of T. If T were a thin triangular metal plate
with uniform density then P would be its centre of mass.

Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

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