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A piece of cheese is located at (12, 10) in a coordinate plane. A mous 14 Mar 2019, 02:54
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Difficulty:

95% (hard)

Question Stats:

41% (02:49) correct 59% (02:28) wrong based on 59 sessions

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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?

(A) 6
(B) 10
(C) 14
(D) 18
(E) 22
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B
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A piece of cheese is located at (12, 10) in a coordinate plane. A mous 14 Mar 2019, 05:39
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Bunuel
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?

(A) 6
(B) 10
(C) 14
(D) 18
(E) 22
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plot on graph values
y=-5x+18
at y=3 ,x = 3; distance 12-3= 9 ; nearing cheese
y=8, x= 2 ; distance 12-2 = 10; going far
sum = 8+2 ; 10
IMO B
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A piece of cheese is located at (12, 10) in a coordinate plane. A mous 01 Apr 2019, 01:13
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we are looking for the intersect between line y = − 5x + 18 and it's perpendicular wich go through (12, 10)
becase the distance is the smallest at this intersect ,the distance will be longer after this intersect , let's call it M
y = − 5x + 18
the perpindicular will have m=1\5
y = 1\5x +p
since it pass through (12, 10) , we can write :
10 = 1\5(12) +p >> p = 38/5

y = 1\5x + 38/5 (1)
y = − 5x + 18 (2)
solving : we get x=2 ,y=8
ans B
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A piece of cheese is located at (12, 10) in a coordinate plane. A mous 08 Mar 2025, 00:57
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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?

The point closest to point (12,10) from the line y=-5x+18 is perpendicular to the line at (a, b).

Slope of line connecting (12,10) & (a, b) = m1 = (10-b)/(12-a)
Slope of line {y = - 5x + 18} = m2 = - 5
Since these lines are perpendicular to each other,
m1 * m2 = -1

(10-b)/(12-a) * (-5) = -1
50 - 5b = 12 - a
a = 5b - 28

Since (a, b) is on the line y = - 5x + 18, it should satisfy it.
b = - 5a + 18

a = 5(-5a+18) - 38 = -25a + 90 - 38 = 52 - 25a
a = 52/26 = 2

b = - 5a + 18 = 8

a + b = 2 + 8 = 10

IMO B
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