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
Lina20 [59]
4 years ago
11

A segment in the complex plane has a midpoint at –1 + i. If the segment has an endpoint at –5 – 7i, what is the other endpoint?

Mathematics
2 answers:
Ket [755]4 years ago
5 0
The midpoint formula is simply
ma = (a1 + a2)/2
mb =(b1 + b2)/2
The midpoint is -1 + i and the other endpoint is -5 - 7i
The other endpoint is
-1 = (-5 + a2)/2
a2 = 3
1 = (-7 + b2)/2
b2 = 9

3 + 9i
morpeh [17]4 years ago
4 0

Answer:

The other end point is: s+ti = 3+9i

Step-by-step explanation:

Mid-Point(M) in the complex plane states that the midpoint of the line segment joining two complex numbers a+bi and s+ti is the  average of the numbers at the endpoints.

It is given by:    M = \frac{a+s}{2} +(\frac{b+t}{2})i

Given: The midpoint = -1 + i and the segment has an endpoint at -5 - 7i

Find the other endpoints.

Let a + bi = -5 -7i  and let other endpoint s + ti (i represents imaginary )

Here, a = -5 and b = -7 to find s and t.

then;

-1+i = \frac{-5+s}{2} + ( \frac{-7+t}{2})i     [Apply Mid-point formula]

On comparing both sides

we get;

-1 = \frac{-5+s}{2}  and  1 = \frac{-7+t}{2}

To solve for s:

-1 = \frac{-5+s}{2}

or

-2 = -5+s

Add 5 to both side we have;

-2+5 = -5+s+5

Simplify:

3 = s or

s =3

Now, to solve for t;

1 = \frac{-7+t}{2}

2 =-7+t

Add 7 to both sides we get;

2+7 = -7+t+7

Simplify:

9 = t

or

t =9

Therefore, the other end point (s+ti) is, 3+9i




You might be interested in
Factor the polynomial as a product of linear factors with complex coefficients.
shepuryov [24]

Answer:

The function

f(x) = x3 + 2x2 − x − 2

is a trinomial and it is expected that it has three factors corresponding to the three roots. The possible roots could 1, -1, 2, or -2. Trying out 1

f(1) = 1 + 2 - 1 - 2 = 0

According to the remainder theorem (x - 1) is a factor. By doing synthetic division

1 | 1 2 -1 -2

      1  3  2

    1  3 2  0

f(x) = (x - 1)(x2 + 3x + 2)

which can further be factored into

f(x) = (x -1)(x +1)(x + 2)

The three factors are

x-1

x+1

x+2

which are all linear expressions

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Find the area of a circle whose circumference measures 28 centimeters.
vagabundo [1.1K]
Assume the radius is R.

2*pi*R = 28 -> R = 14/pi

So the area will be pi*R^2 = 196/pi
7 0
3 years ago
Read 2 more answers
The quotient of a number and 2 is 3. Find the number.
tatiyna

Answer:

6

Step-by-step explanation:

6 divided by 2 is 3

5 0
3 years ago
Which especially shows the distance on a number line between -3 and -10
NNADVOKAT [17]
I need the visuals to accurately answer your question. ;-;
8 0
3 years ago
Consider the following sets of matrices: M2(R) is the set of all 2 x 2 real matrices; GL2(R) is the subset of M2(R) with non-zer
defon

Answer:

Step-by-step explanation:

REcall the following definition of induced operation.

Let * be a binary operation over a set S and H a subset of S. If for every a,b elements in H it happens that a*b is also in H, then the binary operation that is obtained by restricting * to H is called the induced operation.

So, according to this definition, we must show that given two matrices of the specific subset, the product is also in the subset.

For this problem, recall this property of the determinant. Given A,B matrices in Mn(R) then det(AB) = det(A)*det(B).

Case SL2(R):

Let A,B matrices in SL2(R). Then, det(A) and det(B) is different from zero. So

\text{det(AB)} = \text{det}(A)\text{det}(B)\neq 0.

So AB is also in SL2(R).

Case GL2(R):

Let A,B matrices in GL2(R). Then, det(A)= det(B)=1 is different from zero. So

\text{det(AB)} = \text{det}(A)\text{det}(B)=1\cdot 1 = 1.

So AB is also in GL2(R).

With these, we have proved that the matrix multiplication over SL2(R) and GL2(R) is an induced operation from the matrix multiplication over M2(R).

7 0
3 years ago
Other questions:
  • When x=6, what kind of line do you have? Horizontal or vertical
    10·2 answers
  • PLZZZZZZZ ANYONE I NEED HELP WITH THIS IAM SO MAD THAT I CANT GT THISSSS ANSWER :/
    7·2 answers
  • Write he ratio that compares $7 1/2 dollars to 3/4 pound of coffee dollars to pounds of coffee=
    5·1 answer
  • HELP ASAP!
    6·1 answer
  • Help me fill this out thanks
    11·1 answer
  • I need help with this algebra problem​
    15·1 answer
  • The length of a rectangle is 10x² – 13x - 3 / 4x + 3 and the width is 4x² + 11x + 6 / 2x - 3 inches. Find the area of the rectan
    5·1 answer
  • How do i make m the subject of this formula.<br> y=3mt-a^2m
    9·1 answer
  • Its a angle question.<br><br> PLS HELP
    5·1 answer
  • What is -0.4 times -5/6?
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!