Math Is Fun Forum

sologuitar

Member

Registered: 2022-09-19

Posts: 467

Equilateral Triangle

An equilateral triangle is one in which all three sides are of equal length. If two vertices of an equilateral triangle are (0, 4) and (0, 0), find the third vertex. How many of these triangles are possible?

Seeking the needed steps here.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,196

Re: Equilateral Triangle

If we take (0,4) and (0,0) as the two points defining the base then the midpoint is (0,2) and the horizontal line y=2 is the line of symmetry that goes through the vertex.  So it must have its y coordinate 2.

If you use Pythag. on the half triangle made by splitting the equilateral triangle in two along that line (y=2) you can determine the required x coordinate(s).  There will be two answers as the triangle may 'sit' left of the y axis or right of it.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,823

Re: Equilateral Triangle

This interactive tool of MIF's may help visualise what's going on: Interactive Cartesian Coordinates

It has several options you can choose from (eg, regular or irregular shapes, choice of the number of sides, entry of custom coordinates).

However, it will only display one shape at a time, and, unlike Geogebra, it lacks mathematical precision...but it's accurate enough to give a pretty good idea.

Last edited by phrontister (2023-10-14 10:24:18)

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sologuitar

Member

Registered: 2022-09-19

Posts: 467

Re: Equilateral Triangle

If we take (0,4) and (0,0) as the two points defining the base then the midpoint is (0,2) and the horizontal line y=2 is the line of symmetry that goes through the vertex.  So it must have its y coordinate 2.

If you use Pythag. on the half triangle made by splitting the equilateral triangle in two along that line (y=2) you can determine the required x coordinate(s).  There will be two answers as the triangle may 'sit' left of the y axis or right of it.

Bob

Thank you. I will work this out on paper.

sologuitar

Member

Registered: 2022-09-19

Posts: 467

Re: Equilateral Triangle

This interactive tool of MIF's may help visualise what's going on: Interactive Cartesian Coordinates

It has several options you can choose from (eg, regular or irregular shapes, choice of the number of sides, entry of custom coordinates).

However, it will only display one shape at a time, and, unlike Geogebra, it lacks mathematical precision...but it's accurate enough to give a pretty good idea.

Thank you for the link. I truly appreciate your reply.