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Rainbow [258]
2 years ago
5

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.

Mathematics
2 answers:
FromTheMoon [43]2 years ago
4 0
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)
Serhud [2]2 years ago
3 0

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)

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