Answered: what is the equation for a triangle…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter2: Parallel Lines

Section2.6: Symmetry And Transformations

Problem 8E

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what is the equation for a triangle that has a line of symmetry on the x axis and a base on the y axis

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°).

Expert Solution

Step 1

The triangle is symmetric to the x-axis. therefore, the triangle is an isosceles triangle. The equation of the line symmetric to the x-axis is the modulus function. Determine the modulus function for the equal sides of the isosceles triangle.

$L e t t h e s l o p e o f t h e l i n e b e m a n d t h e y - i n t e r c e p t b e b u n i t s . T h u s, e q u a t i o n o f t h e l i n e w i t h s l o p e m a n d y - i n t e r c e p t i s y = m x + b . N o w, t h e m o d u l u s e q u a t i o n f o r t h e l i n e s y m m e t r i c t o x - a x i s i s |y| = m x + b . T h u s, e q u a t i o n o f t h e s i d e s s y m m e t r i c t o x - a x i s i s |y| = m x + b .$

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