Question

Two friends work at different buildings on opposite sides of the city. They would like to meet for coffee after work someplace in between both locations. One friend works 9 blocks west and 6 blocks south of the center of town. The other friend works 9 blocks east and 4 blocks north of the center of town. Which restaurant is closest to the midpoint of the two locations?

Answer 1

A.
Restaurant Casa, which is 1 block south of the center of town
B.
Pizza di Franco, which is 9 blocks north and 5 blocks west of the center of town
C.
Cafe Rosa, which is 2 blocks north and 2 blocks east of the center of town
D.
7th St. Market, which is 2 blocks south and 3 blocks east of the center of town

Answer 2

Do you have a picture?

Answer 3

no

Answer 4

can yu still help tho?

Answer 5

I am trying to solve the problem.

Answer 6

Do you know what coordinate is the center town?

Answer 7

no sir

Answer 8

You don't have to call me sir. I am not one.

Answer 9

oh okay lol

Answer 10

Are you learning slopes?

Answer 11

distance and midpoint

Answer 12

I am just asking just in case if there is anything that this problem is related to.

Answer 13

not slopes

Answer 14

One minute, I am almost getting there.

Answer 15

Do you know the Pythagorean Theorem?

Answer 16

yes a^2+b^2=c^2

Answer 17

Great. I have put an attachment. You can see that the coordinate grids can show it as a triangle. Find the distance of both the legs to get a and b in the pythagorean theorem.

Answer 18

Got it?

Answer 19

no...

Answer 20

You can see a triangle right?

Answer 21

yes

Answer 22

What I have just did was connect the two coordinate dots.

Answer 23

can i have the coordinates

Answer 24

or what ever i need to put in the formua

Answer 25

Well I got it as (9, -6) and (9, 4).

Let's consider the center town that have the coordinates of (0, 0). If you move nine spaces both to the left and to the right or six spaces down or four spaces up.

Answer 26

To find d, which is basically the hypotenuse, you need to figure out a and b. That is the distance of both of the legs.

Answer 27

wait are yu saying i need to use the distance formula

Answer 28

You need to use the Pythagorean Theorem.

Answer 29

but thats a+b

Answer 30

Yes, you just need to find the number of units.

Answer 31

That way you can replace a and b for a value.

Answer 32

this sounds like d= (x1-x2) + (y1-y2)

Answer 33

Yes, or \[\\ d=\sqrt{\left ( x_{2}-x_{1} \right )^{2}+\left ( y_{2}-y_{1} \right )^{2}} \\\]

Answer 34

yeah but

Answer 35

The easiest way is the Pythagorean Theorem in my opinion.

Answer 36

Find the units in A and B.

Answer 37

Leg A has 18 units
Leb B has 10 units.

\[18^2 + 10^2 = c^2\]

Answer 38

oh okey

Answer 39

is it 36+20=c^2

Answer 40

so 56=c^2

Answer 41

18 x 18 = 324
10 x 10 = 100

324 + 100 = 424

Square root of 424 ~ 20.59 ~ 21

Answer 42

holy cow

Answer 43

but where are the corrdinates

Answer 44

this didnt solve anything

Answer 45

You don't need them in the Pythagorean Theorem.

Answer 46

how do i get my answer

Answer 47

So let's say 20 is the midpoint.

Answer 48

40 and -40

Answer 49

If you look closely then it shows that the -1, under the 0, is the closest to the midpoint.

Answer 50

Looking at this from a general point of view.

Answer 51

I would say that this would be A.

Answer 52

okay? but yu cant walk negative blocks

Answer 53

Not really.

Answer 54

But I never mentioned -40 though.

Answer 55

Hopefully A is the answer. I just learned this new with you.

Answer 56

yeah but yu said midpoint idk

Answer 57

Yeah

Answer 58

oh okay well thank yu

Answer 59

Midpoint of -40 and 40 = 0, not 20.

Midpoint of 0 and 40 = 20