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?
Answers
Answer:
222/13
150/13
Step-by-step explanation:
A piece of cheese is located at (12, 10) in a coordinate plane
Question will be either
A mouse is at (4, 2) and is running up the line y = 5x - 18
or A mouse is at (-4, -2) and is running up the line y = 5x + 18
slope = 5
Case 1 : 5x - 18
At the point (a, b) the mouse mouse is closest to Cheese
line between (a, b) & (12, 10) would be perpendicular to the y = 5x - 18
slope = (10 -b)/(12 - a)
5 * (10-b)/(12 - a) = - 1
=> 50 - 5b = a - 12
=> a + 5b = 62
b = 5a - 18 using y = 5x - 18
=> a + 5(5a - 18) = 62
=> 26a = 152
=> a = 76/13
b = 5 * 76/13 - 18 =146/13
a + b= 76/13 + 146/13 = 222/13
case 2 : y = 5x + 18
a + 5b = 62
b = 5a + 18
=> a + 5(5a + 18) = 62
=> 26a = -28
=> a = - 14/13
b = 5(-14/13) + 18 = 164/13
a + b = -14/13 + 164/13 = 150/13
Answer:
When mouse moves away from (a,b) it is getting farther from cheese means that distance between (a,b) and (12,10) is the shortest distance.
so, (a,b) ( 12,10) and ( 4, -2) form a right angle triangle.
Step-by-step explanation:
Answer:
When mouse moves away from (a,b) it is getting farther from cheese means that distance between (a,b) and (12,10) is the shortest distance.
so, (a,b) ( 12,10) and ( 4, -2) form a right triangle.
As (a,b) is a point on 5x+y = 18 , we get 5a +b =18 or
b = 18 -a.
Now using Pythagoras theorem problem can be solved.
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