+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?
+9479 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. 
+9479 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.
+129852 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....!!!!
