+0  
 
0
142
2
avatar+10 

A music company has a stores in Abby (-3, -2) and Cardenas (3, 6). Find each unit of the coordninate plane represents 1 mile.

 

a. The company president wants to build a warehouse that is equdistant from the two stores. Write an equation that describes the possible locations.

 

b. A straight road connects Abby and Cardenas.. The warehouse will be located exactly 4 miles from the road. How many locations are possible?

 

c. To the nearest tenth of a mile, how far will the warehouse be from each store?

NiteWolf813  Jan 24, 2018
edited by NiteWolf813  Jan 24, 2018

Best Answer 

 #1
avatar+7070 
+1

a.

 

distance between warehouse and Abby   =   distance between warehouse and Cardenas

 

Let  (x, y)  be the coordinates of the warehouse.

 

distance between  (x, y)  and  (-3, -2)   =   distance between  (x, y)  and  (3, 6)

 

√[  (x + 3)2 + (y + 2)2 ]   =   √[  (x - 3)2 + (y - 6)2  ]

 

(x + 3)2 + (y + 2)2   =   (x - 3)2 + (y - 6)2

 

x2 + 6x + 9  +  y2 + 4y + 4   =   x2 - 6x + 9  +  y2 - 12y + 36

 

6x + 4y + 4   =   -6x - 12y + 36

 

16y   =   -12x + 32

 

y  =  -3/4x + 2         The warehouse can be any point along this line.

 

Here's a graph:      https://www.desmos.com/calculator/eenwtk2dms

 

b.

 

The warehouse needs to be on the line   y = -3/4x + 2   and needs to be  4  units away from the road. So there are two possible locations.

 

*edit*

c.

 

I think the answer to this part is  6.4  miles, but I don't have a good explanation. sad

hectictar  Jan 24, 2018
edited by hectictar  Jan 24, 2018
 #1
avatar+7070 
+1
Best Answer

a.

 

distance between warehouse and Abby   =   distance between warehouse and Cardenas

 

Let  (x, y)  be the coordinates of the warehouse.

 

distance between  (x, y)  and  (-3, -2)   =   distance between  (x, y)  and  (3, 6)

 

√[  (x + 3)2 + (y + 2)2 ]   =   √[  (x - 3)2 + (y - 6)2  ]

 

(x + 3)2 + (y + 2)2   =   (x - 3)2 + (y - 6)2

 

x2 + 6x + 9  +  y2 + 4y + 4   =   x2 - 6x + 9  +  y2 - 12y + 36

 

6x + 4y + 4   =   -6x - 12y + 36

 

16y   =   -12x + 32

 

y  =  -3/4x + 2         The warehouse can be any point along this line.

 

Here's a graph:      https://www.desmos.com/calculator/eenwtk2dms

 

b.

 

The warehouse needs to be on the line   y = -3/4x + 2   and needs to be  4  units away from the road. So there are two possible locations.

 

*edit*

c.

 

I think the answer to this part is  6.4  miles, but I don't have a good explanation. sad

hectictar  Jan 24, 2018
edited by hectictar  Jan 24, 2018
 #2
avatar+86859 
+2

Here's an explanation for  "c"

 

We have two possible congruent right triangles.....

 

The midpoint   of these two coordinates is  (0,2) ......the distance from this point to either store is

 

sqrt [ (3- 0)^2 + (6 - 2)^2 ]  =  sqrt (9 + 16)  = sqrt (25)  =  5 miles

 

And this is one leg of either right triangle......and the other leg is the distance from the warehouse to the road  = 4 miles

 

So.....the distance from  the warehouse to either store is the hypotenuse of these triangles

 

sqrt (  5^2  + 4^2)  =  sqrt ( 41)  =  6.4 miles

 

JUST AS HECTICTAR FOUND....!!!!

 

 

cool cool cool

CPhill  Jan 24, 2018
edited by CPhill  Jan 24, 2018

6 Online Users

avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.