McDougal Littell Jurgensen Geometry: Student Edition Geometry

5th Edition

ISBN: 9780395977279

Author: Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

Publisher: Houghton Mifflin Company College Division

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Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on …

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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°).

Chapter E, Problem 13.12EX

To determine

To find the third vertices of equilateral triangle, whose other vertices are $(r, 0)$ and $(−r, 0)$ .

Expert Solution & Answer

Answer to Problem 13.12EX

Option (b)

Explanation of Solution

Given information: Vertices of the triangle are: $(r, 0)$ and $(−r, 0)$ .

Concept used:

The distance between the points $(x1,y1)$ and $(x2,y2)$ is

$(x2−x1)2+(y2−y1)2$

Let ABC be the triangle with vertices as $A(r, 0), B(−r, 0)$ and $C(a, b)$ .

Using distance formula,

$AB=4r2=2r; BC=(a+r)2+b2; AC=(a−r)2+b2$

For an equilateral triangle, AB = BC = AC

$(a+r)2+b2=(a−r)2+b2a2+r2+2ar+b2=a2+r2−2ar+b24ar=0⇒ a=0$

Also,

$r2+b2=4r2r2+b2=4r23r2=b2b=r3$

Hence, the third coordinate of the equilateral triangle is $(0, r3)$ .

Chapter E, Problem 13.11EX

Chapter E, Problem 14.1EX

Chapter E Solutions

McDougal Littell Jurgensen Geometry: Student Edition Geometry

Ch. E - Prob. 1.1EX Ch. E - Prob. 1.2EX Ch. E - Prob. 1.3EX Ch. E - Prob. 1.4EX Ch. E - Prob. 1.5EX Ch. E - Prob. 1.6EX Ch. E - Prob. 1.7EX Ch. E - Prob. 1.8EX Ch. E - Prob. 1.9EX Ch. E - Prob. 1.10EX

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To find the third vertices of equilateral triangle , whose other vertices are ( r , 0 ) and ( − r , 0 ) .