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
uranmaximum [27]
3 years ago
12

A line segment has endpoints at (4, –6) and (0, 2). What is the slope of the given line segment? What is the midpoint of the giv

en line segment? What is the slope of the perpendicular bisector of the given line segment? What is the equation, in slope-intercept form, of the perpendicular bisector?
Mathematics
2 answers:
Zigmanuir [339]3 years ago
7 0
1) slope = (y₂-y₁)/(x₂-x₁)

Let A and B be A(4,-6) and B(0,2) ; 

m = [2-(-6)]/[0-4) = (2+6)/(-4) → m = -2 

2) Midpoint = value of x of the midpoint = (x₁+x₂)/2
value of y of the midpoint = (y₁+y₂)/2

x(midpoint) =  (4+0)/2  → x= 2
y(midpoint) =  (-6+2)/2 → y= - 2, so Midpoint M(2,-2)

3) Slope of the perpendicular bisector  to AB:
The slope of AB = m = -2
Any perpendicular to AB will have a slope m' so that m*m' = -1 (or in other term, the slope of one is inverse reciprocal of the second, then if m =-2, then m' = +1/2 ; Proof [ (-2)(1/2) = -1]

4) Note that the perpendicular bisector of AB passes through the midpoint of AB or M(2,-2). Moreover we know that the slope of the bisector is m'= 1/2
The equation of the linear function is :

y = m'x + b or y = (1/2)x + b. To calculate b, replace x and y by their respective values [in M(-2,2)]

2= (1/2).(-2) + b → 2 = -1 + b → and b= 3, hence the equation is:

y = (1/2)x + 3

QveST [7]3 years ago
5 0

Answer:

-2

(2,-2)

1/2

y=(1/2)x-3

You might be interested in
I dont know the x of 30-2x=22
zloy xaker [14]

Answer:

4

Step-by-step explanation:

30-22=2x

8=2x

8/2=x

3 0
2 years ago
Read 2 more answers
X/a+x/b=1<br>make x the subject of the formular​
monitta

Answer:

x = \frac{ab}{b+a}

Step-by-step explanation:

Given

\frac{x}{a} + \frac{x}{b} = 1

Multiply through by ab to clear the fractions

bx + ax = ab ← factor out x from each term on the left side

x(b + a) = ab ← divide both sides by (b + a)

x = \frac{ab}{b+a}

8 0
3 years ago
Plz hurry hurrrrrrrrrrrrrrrrry
SIZIF [17.4K]
It is C  parallelogram and rumbus

5 0
3 years ago
Read 2 more answers
Researchers at Gallup were interested in whether there was a decrease in the proportion of nonretirees (in other words, people w
Lera25 [3.4K]

Answer:

A. We have extremely strong evidence to reject H0.

Step-by-step explanation:

Let P be the proportion of non-retirees in 2015 who did not think that Social Security would be able to pay a retirement benefit by the time that they retire.

According to the data null and alternative hypotheses should be:

  • H_{0}: P=0.60
  • H_{a}: P<0.60

Test statistics is -4.29 and p-value of the statistics is p<0.001

At every significance levels higher than 0.001, we can reject the null hypothesis since p<0.001.

8 0
3 years ago
to estimate the height of the jin mao tower in shanghai , a tourist sights the top of the tower form a mirror that is 86.7 meter
Ray Of Light [21]

Answer:

The height of the tower = 420.48 meters

Step-by-step explanation:

For better understanding of the solution, see the figure attached below :

Let the height of the tower be x meters

Now, using the laws of reflection : angle of reflection = angle of incidence

Also, both the tower and the tourist are standing parallel to each other

⇒ ∠A = ∠i ( Alternate interior angles are equal)

Similarly, ∠D = ∠r ( Alternate interior angles)

But, ∠i = ∠r

⇒ ∠A = ∠D

Also, the tourist and the tower is perpendicular to the ground surface.

⇒ m∠B = m∠E = 90°

Now, in ΔABC and ΔDEC

∠A = ∠D (Proved above)

m∠B = m∠E = 90°

So, by AA postulate of similarity of triangles, ΔABC ~ ΔDEC

As the sides of similar triangles are proportional to each other

\frac{AB}{DE}=\frac{BC}{EC}\\\\\implies\frac{1.92}{x}=\frac{0.4}{87.6}\\\\\implies x=\frac{87.6\times 1.92}{0.4}\\\\\bf\implies x = 420.48\textbf{ meters}

Hence, The height of the tower = 420.48 meters

5 0
3 years ago
Other questions:
  • Can you find the cube root of a negative number? If so, it is positive or negative? Explain your reasoning.
    8·1 answer
  • Which is bigger 5/6 or 16/18?
    8·2 answers
  • 6x - 2(x + 4) = 6 + 2x
    5·2 answers
  • Using column b row 4, find the intersection of lombard street and larkin street. imagine you are in a car: head east on lombard
    10·1 answer
  • Isabella is making a display board for the school council elections. the display is 4.25ft by 6 ft rectangle. she needs to add a
    12·1 answer
  • The diagram shows a circle inscribed in a square.
    10·1 answer
  • Thank you in advance!
    15·1 answer
  • PLZ HELP IT WILL HELP A LOT
    8·2 answers
  • The value of expression x<br> 2 + 3x<br> 2 − 5n − 2 when x = 2 is
    12·1 answer
  • Okay last one of these, 15 points xox​
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!