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
amid [387]
2 years ago
7

) Find the coordinates of the point A' which is the symmetric point

Mathematics
1 answer:
soldier1979 [14.2K]2 years ago
7 0

Let, coordinate of point A' is (x,y).

Since, A' is the symmetric point  A(3, 2) with respect to the line 2x + y - 12 = 0.​

So, slope of line containing A and A' will be perpendicular to the line 2x + y - 12 = 0 and also their center lies in the line too.

Now, their center is given by :

C( \dfrac{x+3}{2}, \dfrac{y+2}{2})

Also, product of slope will be -1 .( Since, they are parallel )

\dfrac{y-2}{x-3} \times -2  = -1\\\\2y - 4 = x - 3\\\\2y - x = 1

x = 2y - 1

So, C( \dfrac{2y -1 +3}{2}, \dfrac{y+2}{2})\\\\C( \dfrac{2y + 2}{2}, \dfrac{y+2}{2})

Also, C satisfy given line :

2\times ( \dfrac{2y + 2}{2})  + \dfrac{y+2}{2} = 12\\\\4y + 4 + y + 2 = 24\\\\5y = 18\\\\y = \dfrac{18}{5}

Also,

x = 2\times \dfrac{18}{5 } - 1\\\\x = \dfrac{31}{5}

Therefore, the symmetric points isA'(\dfrac{31}{5}, \dfrac{18}{5}) .

You might be interested in
Caitlin makes candles and sells them in her online shop. Tall candles cost $8 each and short candles cost $5 each. last month, s
snow_tiger [21]

Answer:

tall candles = 39

Short candles = 52

Step-by-step explanation:

let tall candles be x

and short candles be y

No. Of candles sold = x + y =91

Money made from candles will be equal to = 8x + 5y = $572

These both are simultaneous linear equations.

x + y =91 ( multiply by 5)

5x + 5y = 455

8x + 5y = $572

Subtract them:

-3x = -117

x = -117/3

x = 39

put value of x in

x + y = 91

39 + y = 91

y = 91 - 39

y = 52

x shows tall candles so they are 39

y shows short candles so they are 52

3 0
2 years ago
I suck at math I need help with it!
muminat

Answer:

ok, I can help. Where's the math problem ?

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Olivia is buying bundles of wood for a campfire.The bundles of wood can't be split up.if each bundle costs $3,how many bundles c
victus00 [196]

Answer:

3    

1 $ left over

Step-by-step explanation:

       

                                 10$

         wood              wood                wood  

           3$                      3$                    3$

          she wood only buy 3 and have 1$ left

3 0
2 years ago
Conner and Jana are multiplying (3568)(39610).
NARA [144]

Step-by-step explanation :

Dado que Conner y Jana se multiplican (3568)(39610). El trabajo de Conner El trabajo de Jana (3568)(39610) = 35 + 968 + 10 = 314618 (3568)(39610) = 35⋅968⋅10 = 345680 ¿Es correcto cualquiera de ellos?

Jana y Conner están multiplicando dos números dados. Así que la pregunta es

                                 3568 x 39610

                                  0000

                                3568x

                            21408xx

                          32112xxx

                        10704xxxx

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

                           141328480

Así que la respuesta correcta es 141328480.

También los números se pueden agrupar como

      3568 = 3000 + 500 + 60 + 8

    39610 = 30000 + 9000 + 600 + 10

Después de agrupar multiplicando ambos términos obtenemos la respuesta requerida.

Así que ninguno de los dos tiene la respuesta correcta.

5 0
3 years ago
Read 2 more answers
Please help me! 15 pts! + Brainliest!
WITCHER [35]

Answer:

D

Step-by-step explanation:

It increased 3 meters every second if you look closely at chart

4 0
3 years ago
Other questions:
  • What is the mathematical relationship between the atomic radius (r) and the lattice parameter (a0) in the BCC structure? a. b. c
    13·2 answers
  • What property is illustrated by this problem 45*0=0
    7·1 answer
  • The area of a rectangle is 54cm.the length is 2cm more than a x and the with is 5cm less than twice x.solve for x
    8·1 answer
  • What is the missing number?
    9·1 answer
  • Find the area of the regular trapezoid. The figure is not drawn to scale. The top side is 4, the bottom side is 7, and both side
    9·1 answer
  • Solve this problem.
    15·1 answer
  • Describe different ways in which a plane might intersect the cylinder and the cross section that results?
    8·1 answer
  • I just need just a little help and I will just answer it
    7·2 answers
  • Which of the following is a false statement? Solid substances need different temperature of heat to melt them. All solid substan
    8·1 answer
  • There are 15 coins, which are nickels and dimes only, in Ediths purse. The total value of the coins in her purse is $1.15. If n=
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!