Question

In equilateral triangle RST, R has coordinates (0, 0) and T has coordinates of (2a, 0). Find the coordinates of S in terms of a.

Answer 1

the x  coordinate of S will be 1/2 * 2a = a.
and since  the half triangle is 30-60-90 the y coordinate will be sqrt3 a

so S  is (a , sqrt3a)

Answer 2

Answer:

The S coordinate :

$(a,\sqrt{3}a)\text{ and }(a,-\sqrt{3}a)$

Step-by-step explanation:

In equilateral triangle RST, R has coordinates (0, 0) and T has coordinates of (2a, 0)

We need to find the third coordinate of triangle RST.

R(0,0)

T(2a,0)

S(x,y)

RT=RS=ST (because RST is an equilateral triangle)

Using distance formula,

$\sqrt{x^2+y^2}=\sqrt{(x-2a)^2+y^2}=2a$

$\sqrt{x^2+y^2}=\sqrt{(x-2a)^2+y^2}$

$x^2=(x-2a)^2$

$x^2=x^2+4a^2-4ax$

$x=a$

$\sqrt{x^2+y^2}=2a$

$x^2+y^2=4a^2$

$y^2=4a^2-a^2=3a^2$

$y^2=3a^2$

$y=\pm \sqrt{3}a$

Hence, The S coordinate : $(a,\pm \sqrt{3}a)$