Question

Alice walks along a road which can be modeled by the equation y=6x, where (0,0) represents her starting point. When she reaches a certain point A, she turns right, so that she is traveling perpendicular to the original road, until she stops at the point (333,0). What was the point A where Alice turned?

Answer 1

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Answer:

(9, 54)

Explanation:

The first road has a slope of 6 on its graph. So, the perpendicular road will have a slope of -1/6, the negative reciprocal of the slope of the original road. Translating that from y=-1/6x the the right by 333 units, the equation of the second road is ...

y = -1/6(x -333)

The point where Alice turned is the point of intersection of these two equations:

• y = 6x
• y = -1/6(x -333)

Substituting for y, we have ...

6x = -1/6(x -333)

36x = -x +333 . . . . . multiply by 6, eliminate parentheses

37x = 333 . . . . . . . . add x

x = 9 . . . . . . . divide by 37

So, the point where Alice turned is ...

(x, y) = (9, 6·9)

(x, y) = (9, 54)