If a point P(x,y) is the equidistant from the points A(2,3) and B(6,1), find the equation of locus of moving point P.​



please answer it and I will mark your answer as the brainliest..please..!!!

Answers

Answer 1

Answer:

[tex]y=2x-6[/tex]

Step-by-step explanation:

A locus can be defined as a curve or figure formed by all the points satisfying a particular equation of the relation between coordinates.

The condition stated in the question is such that a generic (x,y) point of the curve is equidistant from the points A(2,3) and B(6,1).

The distance d1 from (x,y) to (2,3) is:

[tex]d_1=\sqrt{(x-2)^2+(y-3)^2}[/tex]

The distance d2 from (x,y) to (6,1) is:

[tex]d_2=\sqrt{(x-6)^2+(y-1)^2}[/tex]

Since d1=d2:

[tex]\sqrt{(x-2)^2+(y-3)^2}=\sqrt{(x-6)^2+(y-1)^2}[/tex]

Squaring both sides:

[tex](x-2)^2+(y-3)^2=(x-6)^2+(y-1)^2[/tex]

Operating:

[tex]x^2-4x+4+y^2-6y+9=x^2-12x+36+y^2-2y+1[/tex]

Simplifying all the squares:

[tex]-4x+4x+4-6y+9=-12x+36-2y+1[/tex]

Moving the variables to the left side and the numbers to the right side:

[tex]-4x+12x-6y+2y=36+1-4-9[/tex]

Simplifying:

[tex]8x-4y=24[/tex]

Dividing by 4:

[tex]2x-y=6[/tex]

Or, equivalently:

[tex]\boxed{y=2x-6}[/tex]


Related Questions

Flavia needs to build a fence around her dog house, as illustrated on the coordinate grid below. If each unit represents 1 foot, what is the total length of Flavia’s fence in feet?

Answers

Answer:

I would say your answer is (D

plz help me with this i do not understand math stuff

Answers

Answer: Pink choice: y= -6x -2

Step-by-step explanation:

In order to be parallel, the slope must be the same. You find the slope as the number or fraction connected to x. ("co-efficient" of x in math talk)

In the given equation, that is -6.  (So that knocks out the first two choices)

The other thing to look at is the y-value of the given coordinate,(-1,4)

(The y-value is the second number in the coordinate (x.y) is the pattern)

and compare it to the the last number in the equations in the choices and     Here the Yellow choice has y= -6x + 4 so this line can't pass through the coordinate given, because  +4 in this equation is where the line crosses the y-axis. ("y-intercept"  in math talk)  So yellow choice is out!

The attachment shows what the graphs of the choices look like.

The black line is the correct answer. The given coordinate (-1,4) is the labeled red spot. The blue line is the given equation. (You can see where it "intercepts the y-axis on the +3)   And the green line also has the -6 slope, but misses the point and intercepts the y-axis at 4.)    

I hope the diagram and explanation helps you understand better. It can be confusing.

-13 (q + 4) = 7 q + 16

Answers

Answer:

q=3.4

Step-by-step explanation:

-13q+-52=7q+16

-52=20q+16

-68=20q

-68/20 is -3.4

b) Simplify 2-(3-a) = -4

Answers

Answer:

-1+a

Step-by-step explanation:

2-(3-a) = (2-3-(-a)) = -1+a  

Answer:

a=-3

Step-by-step explanation:

First off subtract 2 from both sides:

-(3-a)=-6

Then distribute the negative:

-3+a=-6

Finally add 3 to both sides:

a=-3

tadah!!

Hope that helps.

someone please help! I’ll give brainliest!!

Answers

The images are similar. The scale factor is 3/4, but may also be 4/3 depending on which image is the original one. I would go with 3/4.

Anyone wanna help?please

Answers

Answer:

x=14

Step-by-step explanation:

(8x-4)+(6x-12)=180

14x-16=180

14x=196

x=14

Select each polynomial expression that could be factored by grouping.​

Answers

Answer:

The 2nd and 3rd option

Step-by-step explanation:

They can be separated into 2 pairs and factored

Which list shows the numbers below in order from least to greatest? −5.9, −234, 5.78, 58%−5.9, −234, 5.78, 58% −234, −5.9, 58%, 5.78−234, −5.9, 58%, 5.78 −5.9, −234, 58%, 5.78−5.9, −234, 58%, 5.78 58%, −234, 5.78, −5.958%, −234, 5.78, −5.9

Answers

-w,p sixteen - um.iy and 12.66

Which relation is also a function?
{(-1, 3), (0, 2), (3, -1), (3, 2)} {(2,-4), (2,-2), (2, 1), (2, 3)}
{(0, 3), (1, 2), (1, 4), (2.1)}
{(-4,-3), (0.-3). (1, -3), (4, -3)}

Answers

Answer:

{(-4,-3), (0, -3,) (1, -3), and (4,-3)}

Step-by-step explanation:

There can only be one y- output for each x-input. Every other answer is a relation because there are multiple y-values for an x-value.

Answer:

The second one.

Step-by-step explanation:

A function can have two of the same inputs, but not two of the same outputs.

In the first one, the output 2 is found more than once.

In the third one, the output -3, is also found more than once.

The second one has completely unique numbers for both the input and output.

[(2r^2t)^3/4t^2]^2 simply

Answers

Answer:

=4r12t10

Step-by-step explanation:

m= -(4+ m) + 2
m=
what’s m?

Answers

Answer:

m = -1

Step-by-step explanation:

m= -(4+ m) + 2

Distribute

m = -4-m+2

m = -2-m

Add m to each side

m+m = -2-m+m

2m = -2

2m/2 = -2/2

m = -1

can u guys help with my one question i have left

Answers

Answer:

Weeks in a Year. A normal year has 365 days, which is 52 Weeks and 1 Day. A leap year has 366 days, which is 52 .

Step-by-step explanation:

hope this helps :)

Answer:

I think 6

Step-by-step explanation:

365/12=30.42

30.42/5= 6.08

Match the equation on the left with its solution(s) on the right.

Answers

x^2=25 is -5,5
(x+2)^2=169 is -15, 11
x^2-49=0 is -7, 7
-5x^2=-500 is -10, 10

Draw diagonals ACand BDon rectangle ABCD. Measure and record the lengths of the diagonals.

Answers

Answer:

Diagonal   Length

AC               7.21

BD              7.21  

Step-by-step explanation:

Answer:

Diagonal  |  Length

AC            |  7.21

BD            |  7.21

Step-by-step explanation:

-edmentum

What is the volume of the cylinder below

Answers

Answer:

I think d or b

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Lucia wishes to advertise her business, so she gives packs of 6 red flyers to each restaurant owner and sets of 4 blue flyers to each clothing store owner. At the end of the day, Lucia realizes that she gave out the same number of red and blue flyers. What is the minimum number of flyers of each color? Flyers

Answers

Answer:

12

Step-by-step explanation:

No. of red flyers = 6

No. of blue flyers = 4

We need to find the minimum number of flyers of each color if she gave out the same number of red and blue flyers. For this we must find the LCM of 6 and 4.

Prime factorization of 6 = 2×3

Prime factorization of 4 = 2×2

Lowest common multiple of 6 and 4 = 12

Hence, there are 12 minimum number of flyers of each color

Slope 6, passing through (-4,2)

Answers

y=6x+26



y-y1=m(x-x1)

y-2=6(x-(-4))

y-2=6x+24

y=6x+24+2

y=6x+26

A store sells new video games for $45 each. Used video games sell for $18 each. Alex is buying 2 new video games and x used video games. Which equation can be used to find y, the total price Alex must pay in dollars?

Answers

Answer:

u = t/18 - 5

Step-by-step explanation:

45n + 18u = t where t is the total price, n is the number of new video games, and u is the number of used video games

plug in two:

90 + 18u = t

solve in terms of u:

18u = t - 90

u = t/18 - 5

can i get a thanks and brainliest please?

The value of x must be greater than
O 0
O 1
O 3
O 7​

Answers

3 Because the length of the two would not have to make it seven so it’s got to be three

Look at the table. Bob ran 3 miles in 18 minutes. Complete the table:

Answers

Answer:

First one, Third one, Fifth one, and the last one too.

Step-by-step explanation:

Answer:

Step-by-step explanation:

First, make a ratio:

18 min/ 3mile = 6 min/mile

now multiply to finish the table:

1: 6

3: 18

5: 30

10: 60

25: 150

Which table represents a function?

Answers

Answer:

The table that starts with (-3, -1)

Step-by-step explanation:

For a table to represent a function the x value has to be different number. Such as, the other tables one has two -5, two -2, two -4 and etc. Do you get it

Answer: the first box

-3       -1

0         0

-2         -1

8          1

Step-by-step explanation:  the x value can not repet it self but the y value can

suppose that there were a positive correlation between the variables u and v. if v is 24 when u is 10, which of these is most likely to be the value of v when u is 20?

Answers

Answer: 48

Step-by-step explanation: I got it wrong and it said the correct answer was 48

What is the factorization of the expression below?
25x^2 - 36
A. (5x+6)(5x-6)
B. (5x-6)(5x-6)
C. (5x- 4)(5x-9)
D. (5x + 4)(5x-9)

Answers

i think its D????????????????????????


5x5 = 25
9 x 4 = 36
- and a + equals a -



Answer: The answer is A, (5x+6)(5x-6)

Step-by-step explanation: The negative and positive 6 will cancel out the regular X, meaning that 25x^2 and -36 are the only numbers left.

3x + 2y + z = 7 2x + 3y - z = 8 5x + y + 2z = 11

Answers

Answer:

x = 3,    y = 0,      z = −2

Step-by-step explanation:

dose anybody know this? could you provide the step by step

Answers

17 people because if they spend $300 the equation 300=5p+215, then subtract 215 on both sides then it would be 85=5p and then you divide 5 by 85 and you have 17 (sorry if i’m wrong!)

Brad sells each cup of lemonade for $0.50 he wrote.

Answers

Answer:

What are we supposed to solve??? its incomplete

Step-by-step explanation:

Use Graphs A-D for Exercises 9-11. During the winter, the amount of water that flows
down a river remains at a low constant. In the spring, when the snow melts, the flow of
water increases drastically, until it decreases to a steady rate in the summer. The flow
then slowly decreases through the fall into the winter. Consider the graphs shown.
A.
B.
Water (gallons per second)
Water (gallons per second)
Season (winter-fall)
Season (winter-fall)
C.
D.
Water (gallons per second)
Water (gallons per second)
Season (winter-fall)
Season (winter-fall)
9. Which graph best represents the given situation?
Graph B
10. Describe the other three graphs.
11. What are possible situations for graphs B, C, and D?

Answers

did u get the awnsers?

write a real world problem that can be solved using the distributive property

Answers

Answer:

10 + 2. 3(10 + 2) = ? something like that I think .

Step-by-step explanation:

This year, there were 25% fewer sunny days than last year. That’s my question.

Answers

If there were 25% fewer sunny days this year than last year, then there were 25% more sunny days last year than this year and the number of sunny days in the coming year is unknown.

what do reflections have that dilation do not

Answers

Answer:

A reflection is the same just on the opposite side a dilation enlarges or enhances it along with flipping it thats what makes them different please give me brainliest.

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