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?

Guest Apr 30, 2019

#1**+1 **

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

CPhill Apr 30, 2019