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
Ivahew [28]
3 years ago
8

Carter drawers one side of equilateral triangle pqr on the coordinate plane at points P(-3, 2) and Q(5, 2). Which ordered pair i

s a possible coordinate of vertex R?
Mathematics
1 answer:
Neko [114]3 years ago
7 0

Given: Two coordinates of an equilateral triangle P(-3, 2) and Q(5, 2).

To find: Coordinate of third vertex R.

Solution: Let us take coordinate of R is (x,y).

Because we are given PQR is an equilateral triangle, all side of the triangle PQR are equal.

We can say PQ = QR = RS.

Let us find equations by using distance formula.

Distance between two coordinates is given by formula

Distance = \sqrt{(x2-x1)^2+(y2-y1)^2}

PQ=\sqrt{(5-(-3))^2+(2-2)^2}  = \sqrt{(5+3)^2+(0)^2} = \sqrt{8^2+0} = \sqrt{64} =8

QR=\sqrt{(x-5)^2+(y-2)^2}  = \sqrt{x^2-10x+25 + y^2-4y+4} = \sqrt{x^2+y^2-10x-4y+29}

RS=\sqrt{(x-(-3)^2+(y-2)^2}  = \sqrt{x^2+6x+9 + y^2-4y+4} = \sqrt{x^2+y^2+6x-4y+13}.

We know, PQ= QR and PQ= RS.

\sqrt{x^2+y^2-10x-4y+29}[/tex] = 8

Squaring both sides, we get

x^2+y^2-10x-4y+29 =64         -------- equation (1)

and \sqrt{x^2+y^2+6x-4y+13}[/tex] = 8

Squaring both sides, we get  

x^2+y^2+6x-4y+13=64            ---------- equation (2).

Subtracting equation 2 from equation 1.

[/tex]x^2+y^2-10x-4y+29[/tex] = 64

[/tex]x^2+y^2+6x-4y+13[/tex] = 64

----------------------------------------------------

-16x +16 = 0

Subtracting 16 on both sides ,

-16x +16-16 = 0-16

-16x = -16

Dividing -16 on both sides.

-16x/-16 = -16/-16

x=1.

Plugging x=1 in first equation  

(1)^2+y^2-10(1)-4y+29 = 64

1+y^2-10-4y+29 = 64        (Simplifying)

y^2-4y+20 = 64

Subtracting 64 from both sides.

y^2-4y+20-64 = 64-64

y^2-4y-44 = 0

By using quadratic formula..

y=\frac{-(-4)+\sqrt{(-4)^2-4(1)(-44)} }{2(1)}  and

y=\frac{-(-4)-\sqrt{(-4)^2-4(1)(-44)} }{2(1)} [tex]y=2\left(1+2\sqrt{3}\right),\:y=2\left(1-2\sqrt{3}\right)

In decimal form

y=8.928, -4.928.

Therefore, coordinates of vertex R could be (1, 8.928) or (1, -4.928).


You might be interested in
Segments UV and WZ are parallel with line ST intersecting both at points Q and R respectively
Zanzabum

The <em><u>correct answer</u></em> is:

Corresponding (for both blanks)

Explanation:

Corresponding angles are angles that are in the same relative position to both the parallel line they are on and the transversal.  In this case, SQU and WRS are both above the parallel line they are on and on the same side of the transversal; this makes them corresponding angles.  This also means it is the corresponding angles postulate.

3 0
3 years ago
Read 2 more answers
A machinist can produce 114 parts in 6 minutes. At this rate, how many parts can be produced in 15 minutes?
KonstantinChe [14]

285

just figure out how many is made then multiple that by 15

4 0
3 years ago
Read 2 more answers
A car travels 120 miles in 3 hours how far will it take to travel. 200 miles
docker41 [41]
Find mph
120/3 = 40 mph
200/40 = 5 hours to travel 200 miles
4 0
3 years ago
Read 2 more answers
What is the scientific notation for 140000
vampirchik [111]
You move the decimal point forward until it reaches the one so it looks like this:

1.4 x 10⁵ 

the exponent, 5, just tells you how many spaces the decimal point moved.
6 0
3 years ago
a department store sells a pair of shoes with an 87% markup if the store bought the pair of shoes for $55.25 what is the selling
Pani-rosa [81]
64 dollars. 55.25 divided by .87=63.5, round to nearest dollar and you get 64 dollars
6 0
3 years ago
Read 2 more answers
Other questions:
  • Colton has a stone paperweight composed of a triangular pyramid on top of a triangular prism with the dimensions shown below. Us
    9·1 answer
  • Covert 3.92 into a mixed number in simplest from
    5·2 answers
  • Hello, PLEASE ANSWER ASAP!!! Don't report my question or give me false answers but I'm freaking out. I was biking home from scho
    9·2 answers
  • Need help on this PLEASE It is due at 11:40!!! Today!
    7·1 answer
  • Please answer as soon as possible. Use the graphing tool to graph this system of equations.​
    11·1 answer
  • Flying against the wind, an airplane travels 7760 kilometers in 8 hours. Flying with the wind, the same plane travels 3690 kilom
    12·1 answer
  • Who else is watching the unas annus livestream<br><br>#Wearehere​
    10·2 answers
  • Solve this please asap
    7·2 answers
  • A forestal station receives the locations of two fires, one of them in a forest located 11 Km heading N69°W from the station. Th
    14·1 answer
  • Let F(x)=3x-1 and g(x)=×+2. Findf(g(x)) and g(f(x))
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!