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1. Find the distance between the points (1,1) and (4,7). Express your answer in simplest radical form.

2. A floor plan shows that the exterior of a room has dimensions 12 feet by 17 feet. If the area of the room measured from the interior is only 176 square feet, express the thickness of the surrounding walls in feet. (Assume that the walls have uniform thickness). 
3. What is the sum of the coordinates of the midpoint of the segment with endpoints (6,12) and (0,-6)?

Thanks!

 Jun 11, 2019
 #1
avatar+8724 
+3

1.

 

distance between  (1, 1)  and  (4, 7)  =  \(\sqrt{(4-1)^2+(7-1)^2}\ =\ \sqrt{9+36}\ =\ \sqrt{45}\ =\ 3\sqrt5\)

 

2.

 

Let  x  be the thickness of the walls in feet.  
(12 - 2x)(17 - 2x)  =  176

 

 

204 - 24x  - 34x + 4x2  =  176  
4x2 - 58x + 204  =  176

 

 

4x2 - 58x + 28  =  0  
4x2 - 2x - 56x + 28  =  0

 

 

2x(2x - 1) - 28(2x - 1)  =  0  
(2x - 1)(2x - 28)  =  0

 

 

x = 1/2     or     x = 14  
x  can't be  14  because that would make the walls thicker than the dimensions of the exterior of the room.

 

 

x  =  1/2  is the solution.  
 Jun 11, 2019
 #2
avatar+8724 
+3

3.

 

midpoint of  (6, 12)  and  (0, -6)  =  \(\Big( \frac{6+0}{2},\frac{12+-6}{2}\Big)\ =\ \Big(\frac62,\frac62\Big)\ =\ (3,3)\)

 

sum of coordinates of  (3, 3)  =  3 + 3  =  6

 Jun 11, 2019

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