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A piece of cheese is located at (12, 10) in a coordinate plane. A mouse is at (4, -2) and is running up the line y=-5x+18. At the point (a, b) the mouse starts getting farther from the cheese rather than closer to it. What is a+b? 

 Apr 30, 2019
 #1
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The mouse will be closest to the cheese at the point where a perpendicular line through (12,10) intersects the given line 

 

The slope of the given iine  is -5x....so....the slope of a perpendicular line  = 1/5

 

And we can write the equation of this line passing through  (12,10)

 

So  we have

 

y = (1/5) (x - 12) + 10

y = (1/5)x -12/5 + 10

y = (1/5)x + 38/5....   find the x coordinate of the point we seek by setting the lines equal

 

(1/5)x + 38/5   =  -5x + 18

5x + (1/5)x  = 18 - 38/5

(26/5)x = 52/5

26x  = 52

x  = 2

 

And y  =  -5(2) + 18  = 8

 

So....(a, b)  =  (2,8)     and  a + b  =  10

 

See the graph here :  https://www.desmos.com/calculator/hb1g4nnou4

 

cool cool cool

 Apr 30, 2019

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