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
Crazy boy [7]
2 years ago
11

Universal Studios is looking to expand in Ontario. The new theme park will be located equidistant to

Mathematics
1 answer:
sukhopar [10]2 years ago
7 0
<h3>Answer:  (2, 3)</h3>

===============================================

Explanation:

For now, we're only going to consider Newmarket and Markham, which are points N and M respectively.

Let's find the slope of line NM through use of the slope formula.

m = (y2-y1)/(x2-x1)

m = (3-8)/(7-2)

m = -5/5

m = -1

Line NM has a slope of -1. Its perpendicular slope is +1 or just 1.

Rule: If the slopes multiply to -1, then the lines are perpendicular.

Or you can apply the negative reciprocal rule to go from -1 to 1.

We'll keep this perpendicular slope in mind for later.

----------------

Now let's find the midpoint of points N and M.

Add up the x coordinates and divide by 2: (x1+x2)/2 = (2+7)/2 = 4.5

Do the same for the y coordinates:  (y1+y2)/2 = (8+3)/2 = 5.5

The midpoint of N and M is at (4.5, 5.5)

The perpendicular line must go through these two points. I'm going to skip a few steps here, but basically we go from y = mx+b to y = x+1 after plugging in those x,y values and the perpendicular m we found earlier.

--------------------

In short, the perpendicular bisector for line segment NM is the equation y = x+1.

If you follow the same steps as the previous two sections, but you apply them for points M and V instead, then you should find that the perpendicular bisector is y = -3x+9. I'm skipping steps here as well.

----------------------

At this point, we have the system of equations

\begin{cases}y = x+1\\y = -3x+9\end{cases}

Let's use substitution to solve for x and y

y = x+1

-3x+9 = x+1

-3x-x = 1-9

-4x = -8

x = -8/(-4)

x = 2

y = x+1

y = 2+1

y = 3

So together, x = 2 and y = 3 pair up to get the ordered pair solution (x,y) = (2,3)

This is the location where the theme park should be placed. Let's say that C = (2,3). I'm using C for center.

You can use the distance formula to confirm that segments CN, CM and CV are all the same length, which would verify that point C is equidistant from all the other points. Furthermore, it means that points N, M and V are all on the same circle centered at C.

I know it says not to use a graph, but it still helps to see what's going on. Also, it's a handy way to confirm the answer. I used GeoGebra to make the graph. See the diagram below.

Side note: you only need 2 perpendicular bisectors to find point C. You could use three, but that's overkill since they all intersect at the same location.

You might be interested in
What is answer to the questions
puteri [66]

Answer:

Meaning

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
What does U mean in geometry
Nata [24]

Answer:

So the union of sets A and B is the set of elements in A, or B, or both. The symbol is a special "U" like this: ∪ Example: Soccer = {alex, hunter, casey, drew}

Step-by-step explanation:

3 0
3 years ago
Which expression is equivalent to 3√x5y<br>what is it?​
daser333 [38]

Answer: 3x^2 √xy

Step-by-step explanation:

5 0
3 years ago
Identify the statement that represents the given algebraic expression.
ollegr [7]

Answer:

n is -32

Step-by-step explanation:

- 17 \times 2 \: equals \:  - 32 \\  - 32 \div 2 \: equals \:  - 17

8 0
3 years ago
What is the length of x? What is the length of EF? Only enter numbers in the answer boxes below:
ioda

Focus on triangles DFC and DFE:

  • They are both right triangles because DF is perpendicular to EC
  • DC=DE
  • DF is a common side

So, the two triangles are congruent. It follows that CF=FE, and in particular

8x=3x+15 \iff 5x=15 \iff x=3

And since x=3, the length of EF is

3x+15=3\cdot 3+15=24

8 0
3 years ago
Other questions:
  • What is 36/540 partial quotients form
    13·1 answer
  • Please help asap!! I need to hand this in!! Need an accurate answer!!
    5·1 answer
  • Combine the like terms to make a simpler expression:<br> 10k + 1 + 8k + 2
    8·1 answer
  • Can someone please help me with this geometry question?
    5·1 answer
  • Plssssssss help solve
    15·2 answers
  • Can someone please give me the answer I will mark u brilliant
    15·1 answer
  • A student got an 80% on a test that had 40 questions on it. How many questions did the student get correct?
    7·1 answer
  • 10 minutes left unit test PLEASE HELPP
    9·2 answers
  • Y - 3 = -2(x -1)<br> How do i do this?
    6·1 answer
  • Please help, What is the nth term rule of the quadratic sequence below?<br> -4,1,12,29,52,81,116
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!