You can put this solution on YOUR website! an equilateral triangle has 3 equal sides and 3 equal angles.
2 of the 3 vertices are (2,1) and (7,1).
the length of the side is equal to which is equal to 5.
all the sides of this triangle will have this length.
the altitude to this triangle will intersect the base and is a median of the base.
this means that the altitude of this triangle will have an x-valued of 4.5 because 4.5 is midway between 2 and 7.
it is 2.5 from 2 and it is 2.5 from 7.
the altitude of this triangle will be found by the following formula:
tan(60) = x/2.5
solving for x, we get:
x = 2.5 * tan(60) which turns out to be 4.330127019.
add 1 to that and you have the y value of the third vertex of the triangle.
the coordinates of the third vertex of the triangle will be:
(4.5,5.330127019).
it's easiest to see this by a picture.
a picture of what i have just told you is shown below:
answer to your question is that the remaining vertex is at (4.5,5.330127019)
the easiest way to find it was to understand that the third vertex was a point on the altitude to the triangle and that the altitude to the triangle bisected the base of the triangle and was perpendicular to it.
bisecting the base made the x value of the altitude equal to 4.5 which became the x value of the third vertex.
finding the height of the altitude involved trigonometry.
once the height was found, it was added to the y value of the base and became the y value of the third vertex.
the fact that the third vertex was on the altitude to the triangle made finding it easy.
it could have been found another way but that would have involved slopes and equations of lines and finding the intersection of those lines which would have provided the same answer only it would have been much more labor intensive.
understanding that the altitude to the triangle led you to the same intersection point made is to much easier.
