1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Rainbow [258]
3 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]3 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]3 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)

You might be interested in
The endpoints of DE and D(-3, y) and x, 6). The midpoint of DE is M(4,2). What is the length of DE.
Natasha_Volkova [10]

If the endpoints of DE where D(-3, y) and E(x, 6) with the midpoint M(4, 2), the length of DE is 16.12 units

The formula for calculating the midpoint is expressed as;

M(x,y)=(\frac{x_1+x_1}{2}, \frac{y_1+y_2}{2})

For the x-coordinate points:

X = -3+x/2

4 * 2 = -3 + x

8 = -3 + x

x = 8 + 3

x = 11

Get the value of y;

2 = y+6/2

y+6 = 2 * 2

y + 6 = 4

y = 4 - 6

y = -2

Hence the coordinates of D and E are D(-3, -2) and E(11, 6)

D=\sqrt{(6-(-2))^2+(11-(-3))^2}\\D=\sqrt{8^2+14^2}\\D=\sqrt{64 + 196}\\D=   \sqrt{260}\\D= 16.12units

Hence the length of DE is 16.12 units

Learn more here; brainly.com/question/22624745

3 0
2 years ago
He lifted 100 kilograms and 132.5 kilograms. What was the combined weight of his lifts in grams?
Olegator [25]
So add them together
100+132.5=232.5 kg

kilograms=1000 grams so
232.5kg=1000 times 232.5 grams

232500 grams
7 0
3 years ago
Thang decided to borrow ​$7000 from his local bank to help pay for a car. His loan was for 3 years at a simple interest rate of
jekas [21]
You need to find 24% of $7000 because that's the total interest over the course of 3 years. The answer is $1680

6 0
3 years ago
Read 2 more answers
A car with a mass of 1,250 kg travels at 2.24 m/s and bumps into a stopped car with a mass of 1,300 kg. After the collision, the
ddd [48]

Answer:

0.57 m/s

Step-by-step explanation:

4 0
3 years ago
Tonya has a small picture with a length of inches. She wants to enlarge the picture by a factor of 7 and frame it. Which of the
Elena L [17]
Enlarge the picture 7 times by inches
3 0
3 years ago
Other questions:
  • Which unit rate is the lowest price per ounce? (5 points)
    6·2 answers
  • What is the value of x in the drawings if we know the triangles are similar?
    5·2 answers
  • Which equation could be used to find the length of the hypotenuse?<br>​
    12·2 answers
  • What is the mode of the following data?
    7·2 answers
  • What is the missing lenghts?
    9·1 answer
  • What is the slope of line that passes through the pair of points (4,7),(7,-2)
    12·1 answer
  • 12 yards +14 feet by 2
    5·1 answer
  • A running track has two straight sides with length 140 m and two semicircle ends with radius 70 m. It takes Kat 40 seconds to jo
    14·1 answer
  • √((2+√3)÷(2-√3))<br><br>what is the answer?​
    13·2 answers
  • Would - (-2) 4 be negative or positive
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!