Question

If the vertices of an equilateral triangle are (3,0) and (6,0) ,find the third vertex.

Answer 1

Answer:

The third vertex is either

( 9 / 2,  3√3 / 2 )  or  ( 9 / 2,  -3√3 / 2 ).

Approximating with decimals, these are approx (4.5, 2.6) and (4.5, -2.6).

I hope this helps you.

Step-by-step explanation:

The equilateral triangle has side length 6-3 = 3.

Half the triangle is a right angled triangle with:

• hypotenuse 3 (one side of the equilateral triangle)
• base 3/2 (half of the base of the equilateral triangle).

Using Pythagoras' Theorem, the height h of the triangle is:

h = √( 3² - (3/2)²) = 3√3 / 2

Since the given triangle sits on the x-axis, the third vertex is either this far above, or this far below, the x-axis.  So the y-coordinate is h or -h.

The third vertex is over the midpoint of (3,0) and (6,0), so its x-coordinate is (3+6)/2 = 9/2

Therefore, the third vertex is either

( 9 / 2,  3√3 / 2 )

or

( 9 / 2,  -3√3 / 2 ).