Write the equation of the perpendicular bisector of the segment formed by:
(-4, 3) and (8, -3)

Answers

Answer 1

Answer:

The equation of perpendicular bisector is:

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

Step-by-step explanation:

Given the points

(-4, 3)(8, -3)

First, we need to find the midpoint of the points (-4, 3) and (8, -3)

[tex]\mathrm{Midpoint\:of\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right)[/tex]

[tex]\left(x_1,\:y_1\right)=\left(-4,\:3\right),\:\left(x_2,\:y_2\right)=\left(8,\:-3\right)[/tex]

[tex]=\left(\frac{8-4}{2},\:\frac{-3+3}{2}\right)[/tex]

[tex]=\left(2,\:0\right)[/tex]

Thus, the midpoint of the points is: (2, 0)

Now, finding the slope between (-4, 3) and (8, -3)

[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\left(x_1,\:y_1\right)=\left(-4,\:3\right),\:\left(x_2,\:y_2\right)=\left(8,\:-3\right)[/tex]

[tex]m=-\frac{1}{2}[/tex]

Therefore, the slope m = -1/2

The slope of the line perpendicular to the segment = [-1] / [-1/2] = 2

Using the point-slope form of the equation of the line, the equation of perpendicular bisector is:

[tex]y-y_1=m\left(x-x_1\right)[/tex]

where m is the slope of the line

substituting the slope 2 and the point (2, 0)

[tex]y-y_1=m\left(x-x_1\right)[/tex]

[tex]y - 0 = 2 (x-2)[/tex]

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

Therefore, the equation of perpendicular bisector is:

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


Related Questions

Division number story with the answer 5/2

Answers

Answer:

I have one below (It's kind of simple though..)

Step-by-step explanation:

Harry Had 5 Potions he made in Potions Class. He would like to share the 5 potions with his 2 friends, Ron and Hermione. How many potions do they each get? Write the equation for how many each person gets in fractional form

(This is a simple one I don't have a complicated one..)

If these two shapes are similar, what is the measure of the missing length w?​

Answers

Answer:

2

Step-by-step explanation:

because 8 and 4 to get the shape smaller you divide it by 2 so you times 1 *2 to get the bigger one

Help please.
Algebra.

Answers

Answer:

3) B

4) D

5) C

Step-by-step explanation:

3) Slope is before X

4) Set equal to Y

5) Use rise over run to find slope then find y intercept

"what quadrant is...." PLEASE PLEASE HELP!!!! Thank you so so much!!! *will give brainliest*

Answers

Given:

[tex]\tan \theta > 0[/tex] and [tex]\sec \theta <0[/tex].

To find:

The quadrant.

Solution:

We know that,

In I quadrant, all trigonometric ratios are positive.

In II quadrant, only [tex]\sin \theta, \text{cosec}\theta[/tex] are positive and others are negative.

In III quadrant, only [tex]\cot \theta, \tan\theta[/tex] are positive and others are negative.

In IV quadrant, only [tex]\cos \theta, \sec\theta[/tex] are positive and others are negative.

We have,

[tex]\tan \theta > 0[/tex] and [tex]\sec \theta <0[/tex].

Here, [tex]\tan \theta[/tex] is positive and [tex]\sec \theta[/tex] is negative. So, [tex]\theta [/tex] lies in the III quadrant.

Therefore, the correct option is C, i.e., III.



Help
Me
Solve
This

Answers

Answer:

POG

Step-by-step explanation:

Answer:

Step-by-step explanation:

Nsjsjsjsms

Find the length of the tangent segment AB to the circles centered at O and O' whose radii are a and b respectively when the circles touch each other

Answers

Answer:

[tex]AB=2\sqrt{ab}[/tex]

Step-by-step explanation:

From figure,

[tex]OA=a, \quad \quad O'B=b\\\Rightarrow OO'= (a+b) \quad \quad \text{and}\quad OD=(a-b)[/tex]

In triangle [tex]OO'D[/tex]

  [tex](OO')^2=(OD)^2+(O' D)^2[/tex]

[tex]\Rightarrow (a+b)^2=(a-b)^2+(O' D)^2\\\Rightarrow a^2+b^2+2ab-a^2-b^2+2ab=(O' D)^2\\\Rightarrow 4ab=(O' D)^2\\\Rightarrow O'D=2\sqrt{ab} \\\Rightarrow O' D=2\sqrt{ab}=AB \quad \quad [\because O' DAB\;\; \text{is a rectangle.}][/tex]

Hence, [tex]AB=2\sqrt{ab}[/tex]

Dakota received a mark of 68% on his math test.
The test had 25 questions.
How many questions did Dakota answer correctly?

Answers

Dakota answered 17 questions correctly.
Dakota answers 17 questions right

solve the following system of equations​

Answers

-9x+12y=15
-10x+12y=6

x=9

-81+12y=15
12y=96

y=8

Answer: x = 9 y = 8

evaluate 40 divided by 8 plus 3 multiplied by 4 multiplied bye 2

Answers

Answer:

29

Step-by-step explanation:

40/8 + 3*4*2 =

5 + 12*2 =

5 + 24 =

29

Answer: GIVE ME BRAINLIEST! THANKS!

29

Step-by-step explanation:

CHECK FO YO SELF BOIIII!!!!!!!!

Help 39 point pic below Math

Answers

Step-by-step explanation:

Remember the Difference of Squares:

a² - b² = (a + b)(a - b)

Therefore (√20 - √3)(√20 + √3)

= (√20)² - (√3)² = 20 - 3 = 17. (C)

Help plz i hate this but everytime I do this I get it worng

Answers

Answer:

The answer is 19.25

Step-by-step explanation:

Key skills needed: Fraction operations, decimal conversion

1) We are given the hint to use 9 as "b", and we get:

---> [tex]a = \frac{16}{8}(9) + \frac{10}{8}[/tex]  

Let's do  [tex]\frac{16}{8}(9)[/tex]

--> [tex]\frac{16}{8}[/tex] is the same as [tex]16[/tex] ÷ [tex]8[/tex]

16 divide by 8 is 2.

2) This means that it would be  ---> [tex]2(9)[/tex]  which is simply 2 times 9.

2 times 9 = 9 + 9 = 18

3) With that result, it would be  ---> [tex]a = 18 + \frac{10}{8}[/tex]

Now, do [tex]\frac{10}{8}[/tex] (10 divided by 8)  ---> Get 1.25

4) 18 + 1.25 = 19.25, so --> [tex]a = 19.25[/tex] is the answer

Hope you understood and have a nice day!!   :D

a(x + b) = c
make x the subject​

Answers

Answer:

Th answer is x = (c - ab) / a

Step-by-step explanation:

The steps are :

a(x + b) = c

ax + ab = c

ax = c - ab

x = (c - ab) / a

Answer:

x=(c-ab)/a

this s answer

Can someone help me please I need help

Answers

9514 1404 393

Answer:

  1. yes

  2. no

Step-by-step explanation:

We can label the equations [1] and [2] to make the transformations to the equivalent system easier to describe.

1. The equivalent system is [1] +[2] and 2×[1]. Both of these are described as allowed transformations.

  [1] +[2] is (-x +2y) +(-3x +9y) = (10) +(-15)  ⇒  -4x +11y = -5

  2×[1] is 2(-x +2y) = 2(10)  ⇒  -2x +4y = 20

These resulting equations match the ones proposed for the equivalent system.

  yes, the systems are equivalent

__

2. The first equation of the proposed "equivalent" system is [1] +[2]. The second equation has no relation to the equations of the given system.

  [1] +[2] = (-2x +3y) +(-11x -13y) = (14) +(-6)  ⇒  -13x -10y = 8

  no, the systems are not equivalent

(This is also shown in the attached graph. The original system is in red; the "equivalent" system is in green. Equivalent systems have the same solution. These do not.)

pls help :( :) i’m a little lost

Answers

Answer:

B

Step-by-step explanation:

On a graph you go rise over run (or Y divided by X) which in this equation is 1 divided by 2 which equals 1/2. You also need to look at what number is being crossed on the y axis, which in this case is 1. Slope intercept form is y=mx+b with m being the slope (1/2) and b being the y intercept (1)

Answer:

B. y = 1/2x + 1

Step-by-step explanation:

I went ahead and graphed each of the answer options for you and when I graphed for B it gave me:

HEEEEEEEEEEEEEEEEEEEEEEEELLLLLLLLLLLLLLP

1 Evaluate the following algebraic expression: 12 + y4 - 6 When Y=3

Answers

Answer:

your answer would be 6

Step-by-step explanation:

(3)4-6

12-6

6

Answer:

I think it would be 18

Step-by-step explanation:

3 x 4 =12

12 + 12= 24

24 -6=18

13х - 7y + 4х
Please explain and awnser it’s for a test!

Answers

Answer:

17x-7y

Step-by-step explanation:

Im assuming you need to simplify it.

combine 13x and 4x

17x-7y

The table shows the time Merrida spent driving and the number of miles she drove. She drove the same number of miles each hour.

Merrida’s Driving Time and Distance
Miles
Hours
140
4
175
5
210
6

How many miles did she travel each hour?
23 miles per hour
35 miles per hour
42 miles per hour
53 miles per hour

Answers

Answer:

35 miles per hour.

Step-by-step explanation:

140÷4=35

!75÷5=35

210÷6=35

Answer:

❌23 miles per hour

✅35 miles per hour

❌42 miles per hour

❌53 miles per hour

Go follow me on T I k T o k  aiyana_parker

What are the zeros of the function (x) = x2 – 3x+2?

Answers

Step-by-step explanation:

f(x) = x² - 3x + 2 = (x - 2)(x - 1).

When f(x) = 0, (x - 2)(x - 1) = 0.

=> x = 2 or x = 1.

Simplify -4(2c+3) pleaseeeee

Answers

Answer:

-8c -12 =0

-8c = 12

c = - 12/8 = -3/2

Ey can someone answer my question please cause i've posted it a few times and nothing happen

Answers

Answer:

we could migrate here

Step-by-step explanation:

Answer:

I feel like I answered this before

Step-by-step explanation:

Find the solution to the system of linear equations below.

x - y = 0
3x + 2y = 10

Answers

Answer:

the desired solution is (2, 2)

Step-by-step explanation:

Solve this using elimination by add'n/subtr'n.

Multiply the first equation by 2, obtaining the equivalent set of equations:

2x - 2y = 0

3x + 3y = 10

Combining like terms, we get 5x = 10, and thus x must be 2.

Subbing 2 for x in the first equation yields 2 - y = 0, or y = 2.

Then the desired solution is (2, 2).

Factor f(x) 3x^3-4x^2-28x-16 given that (x+2) is a factor

Answers

Step-by-step explanation:

3x³ - 4x² - 28x - 16

= (x + 2)(Ax² + Bx + C)

= Ax³ + (2A + B)x² + (2B + C)x + 2C.

By Comparing Coefficients, we have:

A = 3,2A + B = -4,2B + C = -28,2C = -16.

Solving them will give A = 3, B = -10 and C = -8.

Hence 3x³ - 4x² - 28x - 16

= (x + 2)(3x² - 10x - 8)

= (x + 2)(3x + 2)(x - 4).

The answer is f(x) = (x + 2)(3x + 2)(x - 4).

$250.00 memberships were discounted 56%! Do you know how much I'll pay for that membership now?

Answers

Answer:

Step-by-step explanation:

to find out you will

250*56/100=140 this is the discount

250-140=110 you will pay for membership

Answer: 110 %

Step-by-step explanation:

there is a ratio of 5 girls to 3 boys in the chorus.there are 24 boys in the chorus.how many girls are in chorus

Answers

Answer:

40

Step-by-step explanation:

3 x 8 = 24

5 x 8 = 40

24/3 = 8

5 x 8 = 40

There are 40 girls

2. (7.3B)Gwen has $29.00. If she buys 2 shortcakes at $3.99 each and 7 pounds of strawberries
for $7.67 from the grocery store, how much money will Gwen have left in dollars and cents ?
A) $14.00
B) $32.99
C) $20.50
D) $13.35

Answers

Answer:

d. $13.35

Step-by-step explanation:

subtract

i am so sorry if this is wrong! hope this helps:)

help me someone:((!!!!!

a fruit company delivers its fruit in two types of boxes : large and small. a delivery of 6 large boxes and 5 small boxes has a total weight of 145 kilograms. A delivery of 2 large boxes and 3 small boxes has a total weight of 57 kilograms. how much does each type of box weigh?​

Answers

Answer:

Hope this helps!

Step-by-step explanation:

2L + 3S = 83

 

4L + 8S = 197

 

Multiplies the top equation by -2.

-4L + -6S = -166

 

4l  + 8S = 197

 

 

Adding them together...

 

2S = 31

 

S = 31/2 = 15.5

 

Plugging into the first equation:

 

 2L + 3S = 83

 

 2L + 3(15.5) = 83

 

2L + 46.5 = 83

 

2L = 83 - 46.5

 

2L = 36.5

 

L = 36.5/2 = 18.25

 

check:

 

2L + 3S = 2(18.25) + 3(15.5) = 36.5 + 46.5 = 83

 

4L + 8S = 4(18.25) + 8(15.5) = 73 + 124 = 197

 

The Large box weighs 18.25

The small box weighs 15.5

what is the image of the point ( -4, 8) after a rotation of 90° counterclockwise about the origin ​

Answers

Answer:(-8,-4)

Step-by-step explanation:

what is 5square times 34 times 10square.

Answers

85000 on the graphing calculator

Answer:

85,000

Step-by-step explanation:

(5 square) *34* (10 square)

Sushil and Fiona win some money and share it in the ratio 4:1. Sushil gets £33 more than
Fiona. How much did they get altogether?

Answers

Sushli 4x
Fiona x
Sushli x+33
X+33=4x
3x=33
x=11

x+4x=5x=£55

the perimeter of Mrs.Moody's rectangular vegetable garden is 66 meters The length is 9 less than twice the width Find the length and width​

Answers

i am sorry if my answer was wrong but i got this .

The total perimeter is 66.
assume the width is x
The length will be 2x - 9 .

Thus ,

(2x-9) + (2x-9) + x + x = 66
2x - 9 + 2x - 9 + 2x = 66
6x - 18 = 66
x = 14

Thus the width is 14 ,
the length is 2x - 9 , 2(14) - 9 = 19

sorry if i give wrong answer .

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