Question
in an equilateral triangle RST, R has coordinates (0.0)and T has coordinate of (2a,0).Find the coordinates of S in terms of a.
Answers
MathMate
By symmetry, S must lie on the vertical line x=a.
Let the coordinates of S be (a,y).
Since the length of one side of the triangle is (2a-0)=2a, we can calculate the distance of (a,y) to (0,0) and equate to 2a accordingly.
Using Pythagoras theorem,
(2a)=sqrt(a²+y²)
Solving for y:
y²=(2a)²-a²=3a²
y=(√3)a
Let the coordinates of S be (a,y).
Since the length of one side of the triangle is (2a-0)=2a, we can calculate the distance of (a,y) to (0,0) and equate to 2a accordingly.
Using Pythagoras theorem,
(2a)=sqrt(a²+y²)
Solving for y:
y²=(2a)²-a²=3a²
y=(√3)a