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
lisabon 2012 [21]
3 years ago
5

Opposite vertices of a rectangular box whose edges are parallel to the coordinate axes are (-5, -6, 3) and (-9, 10, 4) . List th

e coordinates of the other six vertices of the box.
Mathematics
1 answer:
LuckyWell [14K]3 years ago
8 0

Answer:

C=(-9,-6,-3)

D=(-9,10,-3)

E=(-5,10,-3)

F=(-5,10,4)

G=(-5,-6,4)

H=(-9,-6,4)

Step-by-step explanation:

Its always convenient to name the two points; let's name (-5,-6,3) and (-9,10,4) as A and B respectively.

Also, we can say that these points are Position vectors from the origin!

\overrightarrow{OA}=\begin{bmatrix}-5\\6\\3\end{bmatrix},\quad\overrightarrow{OB}=\begin{bmatrix}-9\\10\\4\end{bmatrix}\\

So in order to find the dimensions of the box, we need to find the distance from OA to OB (aka relative distance \overrightarrow{AB})

\overrightarrow{AB}=\overrightarrow{OB}-\overrightarrow{OA}

\overrightarrow{AB}=\begin{bmatrix}-9\\10\\4\end{bmatrix}-\begin{bmatrix}-5\\-6\\3\end{bmatrix}

\overrightarrow{AB}=\begin{bmatrix}-4\\16\\1\end{bmatrix}

Now, why did we do this?

  • the vector AB shows the 'direction to go' from the point A to the point B. Now think of point A as it is on the the origin (0,0,0) and if we move -4 steps in the x direction, 16 steps to the y-direction and 1 step to the z-direction, you'll reach the point B. (the directions can be taken in any order)
  • Another cool thing here is that at each individual direction, you're also crossing other vertices of the box.
  • To find the actual coordinates: just add the coordinates of A to the relative vector positions (don't worry if this is confusing, we'll do this below)

So at the point A, the relative distance from A is (0,0,0)

if you add the coordinates of the point A (-5,-6,3) to (0,0,0) you'll get its original position!

a) If we move -4 steps in the direction of x. The relative distance from A will be: (-4,0,0), this is a vertex of the box.

it's original position will be (-4,0,0) + (-5,-6,3) = (-9,-6,-3), let's call it vertexC.

b) If we move 16 steps more in the direction of y. The relative distance from A will be: (-4,16,0) this is a vertex of the box.

it's original position will be (-4,16,0) + (-5,-6,3) = (-9,10,-3), let's call it vertexD.

If we move 1 step more in the direction of z. The relative distance from A will be: (-4,4,1) this is a vertex of the box.

it's original position will be (-4,16,1) + (-5,-6,3) = (-9,10,4) we're back to our point B.

we have found the coordinates of 2 more vertices of the box in total (we need to find 4 more!). Previously, we first took the x-direction then y and z. now we're gonna take the y-direction first, its a different route, but will also take us to B. This will help us meet the other edges of the box

let's go back to our relative position of A (our starting point). (0,0,0)

c) If we 16 steps in the direction of y. The relative distance from A will be: (0,16,0) this is a vertex of the box.

it's original position will be (0,16,0) + (-5,-6,3) = (-5,10,-3), let's call it vertexE.

d) If we move 1 step more in the direction of z. The relative distance from A will be: (0,16,1) this is a vertex of the box.

it's original position will be (0,16,1) + (-5,-6,3) = (-5,10,4), let's call it vertexF.

if we move in the direction of x, we'll be at B. So we're gonna go back and take another different route. This time, we'll start from the z-direction.

let's go back to our relative position of A (our starting point). (0,0,0)

e) If we move 1 step in the direction of z. The relative distance from A will be: (0,0,1) this is a vertex of the box.

it's original position will be (0,0,1) + (-5,-6,3) = (-5,-6,4), let's call it vertexG.

f) If we move -4 steps in the direction of x. The relative distance from A will be: (-4,0,1), this is a vertex of the box.

it's original position will be (-4,0,1) + (-5,-6,3) = (-9,-6,4), let's call it vertexH.

and we have found all the coordinates of the vertices of the box.!

You might be interested in
How can I solve this?
Mnenie [13.5K]
X-1/3 = y-2/4
4(x-1) = 3(y-2)
4x-4 = 3y-6
4x-3y = -2 --->1
4x +3y =8 ---->2
2-1 ; 6y = 10
y = 10/6 or 5/3
And 4x + 3(10/6) = 8
4x =3
X = 3/4

6 0
3 years ago
Take 56 and divide it by 4
Hunter-Best [27]
The answer will be 9 ok
3 0
3 years ago
Read 2 more answers
DO THIS FAST PLEASE I WILL GIVE BRAINLY CROWN
vekshin1

5 ÷ 1/2 => 5 x 2/1 => 10/1 => 10

8 0
3 years ago
Read 2 more answers
Is x-2 a factor of f(x)=6x^2-7x-5​
Paha777 [63]

Answer:

its not

Step-by-step explanation:

if you do the division euclidiene the rest will be 5 not zero

f(x)=(x-2)(6x+5)+5

7 0
2 years ago
What improper fraction goes with 1 and three fourths
Katyanochek1 [597]
7/4 because you times 4 and 1.then add 3 and you get 7 so 7/4
7 0
3 years ago
Other questions:
  • Element X decays radioactively with a half life of 13 minutes. If there are 530 grams of Element X, how long, to the nearest ten
    5·1 answer
  • 2. Your bank account has -15 in it. You deposit $7 per day.
    15·1 answer
  • Dr. Ibanez recorded the amount of snowfall, in centimeters, at 10 different locations during 1 day and then arranged the amounts
    15·2 answers
  • A fox can run at a speed of 42 miles per hour. How many feet per hour is this? 1 mile=5280 feet
    12·1 answer
  • The sum of three consecutive integers is -324
    14·2 answers
  • What it the unit rate of 183 miles to 3 hours
    10·2 answers
  • After Rockwell farms installed an irrigation system, their yield per acre of corn rose 15% from 150 bushels per acre. what was t
    15·1 answer
  • What is the remainder when 73,847 is divided by 43? Enter your answer as a whole number in the box
    6·1 answer
  • 4. Evaluate 4x + 2 when x = 5<br> O<br> 22<br> 47<br> O<br> 11
    9·2 answers
  • 7x-2y-1= <br><br> The x=3<br> The y is= 4
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!