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
UNO [17]
3 years ago
14

Let A=(-6,7), B=(-4,11), and C=(-2.10) be three points in the coordinate plane (A) Verify that the three points form a right tri

angle, and Identify the point at the vertex where the right angle is. (Make sure to provide thorough explanation/work to justify your answer.) Lletres (1) Determine the equation of the line on which the hypotenuse of the right triangle lles. (e) Determine the coordinates of the midpoint of the hypotenuse.

Mathematics
1 answer:
faust18 [17]3 years ago
8 0

Answer:

  (A) see below

  (B) the right angle is at vertex B(-4,11)

  (1) 3x -4y = -46

  (E) the midpoint is (-4, 8.5)

Step-by-step explanation:

(A) The slope of line AB is Δy/Δx = (11-7)/(-4-(-6)) = 4/2 = 2. The slope of line BC is (10-11)/(-2-(-4)) = -1/2. The slopes of AB and BC have a product of 2(-1/2) = -1, so are the slopes of perpendicular lines. The points are distinct, and lines joining two pairs of them are at right angles, so the points form a right triangle.

(B) Point B(-4,11) is the point of intersection of perpendicular segments AB and BC, so is the location of the right angle.

(1) The slope of the hypotenuse AC is ...

  Δy/Δx = (10-7)/(-2-(-6)) = 3/4

In point-slope form, the equation for the line through point A with this slope is ...

  y -7 = 3/4(x +6) . . . . point-slope form of the equation of the hypotenuse

  4y -28 = 3x +18 . . . . multiply by 4

  -46 = 3x -4y . . . . .  . subtract 18+4y

  3x -4y = -46 . . . . . . . standard form equation of the hypotenuse

(E) The midpoint of the hypotenuse is the average of the endpoint coordinates:

  M = (A + C)/2 = (-6-2, 7+10)/2 = (-4, 8.5)

The midpoint of the hypotenuse is M(-4, 8.5).

You might be interested in
:) PLEASE!!!! HELP! some food while you solve <3
Dominik [7]

Answer:

1/3

Step-by-step explanation:

rise over run. Find two places that land on a line I picked (0,0) and (3,1) then count up one from the first point and over 3 for the second.

6 0
3 years ago
Read 2 more answers
The sum of the first n terms of an arithmetic sequence is n/2(4n + 20).
lesantik [10]

Answer:

(a).

S_{n} =  \frac{n}{2} (4n + 20) \\  \\S _{n - 1} =  \frac{(n - 1)}{2} (4n - 4 + 20) \\  \\ S _{n - 1} =  \frac{(n - 1)}{2} (4n + 16) \\  \\S _{n - 1} = \frac{(n - 1)(4n + 16)}{2}  \\   \\  { \boxed{S _{n - 1} =  {2 {n}^{2} + 6n - 8}}} \\

(b).

from general equation:

S _{n - 1} =  \frac{(n - 1)}{2} (4n + 16)

first term is 4n

common difference:

16 =  \{(n - 1) - 1 \}d \\ 16 = (n - 2)d \\ d =  \frac{16}{n - 2}

8 0
3 years ago
Please help and explain
Sonja [21]

Find out how much over the 10 years whatever it says and then use that to explain if it's worth is

3 0
3 years ago
What’s 1 decade and 8 years minus 9 years
san4es73 [151]
One decade is 10 years+ 8 years is 18 total years
18 minus 9 is 9 years
Hope this helps
6 0
3 years ago
Read 2 more answers
15 POINTS!!! (16*4^3*8^8)^5 Find the answer and show work how you got it
777dan777 [17]

Answer:

2^170

Step-by-step explanation:

(16 x 4^3 x 8^8)^ 5

- start by converting it all to a common base

(2^4 x 2^3 x 2^24)^5

- calculate the product, by adding all the powers

(2^34)^5

= 2^170

5 0
3 years ago
Read 2 more answers
Other questions:
  • at a display boothat a amusment park every visitor gets a gifr bag some of the bags have items in them as shown in the table bel
    15·1 answer
  • Help plzzzz ............
    10·1 answer
  • Addison was given a gift card for a coffee shop. Each morning, Addison uses the card to buy one cup of coffee. Each cup of coffe
    8·1 answer
  • a segment with endpoints A (4,2) and C (1,5) is partitioned by a point B such that AB and BC from a 1:3 ratio. find B.
    8·1 answer
  • Please answer correctly !!!!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!!!!!!
    6·2 answers
  • (6^4)x=6^12 single exponent<br><br> pls help
    7·1 answer
  • Please help me I will give brainliest
    5·1 answer
  • Please help me with this math problem. Only type answer please dont upload files
    10·1 answer
  • (-11x^2 +6) - (14x^2 +2)
    13·1 answer
  • ANSWER QUICKLY PLEASE
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!