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mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Equilateral Triangle

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

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Equilateral Triangle

The third vertex will be directly across from the midpoint of the base (M) , and, as the y axis is that base, it will be on a horizontal  line, drawn from M. That will fix its y coordinate. You'll have to do some trig. to get the x coordinate.

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

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Equilateral Triangle

The third vertex will be directly across from the midpoint of the base (M) , and, as the y axis is that base, it will be on a horizontal  line, drawn from M. That will fix its y coordinate. You'll have to do some trig. to get the x coordinate.

Bob

Trigonometry is several chapters away. The author does not expect students in chapter 1 to solve questions using trigonometry which is located in chapter 5 or 6 of the textbook. What's the algebra way to answer this question?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Equilateral Triangle

Trig includes pythagoras.  Any equilateral triangle can be split into two right angled triangles with a line through the midpoint of the base.  You know the hypotenuse and half the base so you can work out the height, which is the x coordinate of the vertex.

Make a sketch and it should be fairly easy.

Bob

---

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

amnkb

Member

Registered: 2023-09-19

Posts: 253

Re: Equilateral Triangle

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

Equilaterals have all sides the same lenbth

Distance Formula:

so sides' lengths is 4
3rd pt will be 4 units from known pts

Both are equal to 4 so set them equal

Square both sides and solve

Now you need to find x
try with (0,0)

this means that there are 2 triangle that work
(draw the dots to see why this is so)

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Equilateral Triangle

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

Equilaterals have all sides the same lenbth

Distance Formula:

so sides' lengths is 4
3rd pt will be 4 units from known pts

Both are equal to 4 so set them equal

Square both sides and solve

Now you need to find x
try with (0,0)

this means that there are 2 triangle that work
(draw the dots to see why this is so)

I will continue with this problem on paper.