dhairya275 wrote:The equation of line n is y = (4/3)x - 100. What is the smallest possible distance in the xy-plane from the point with coordinates (0, 0) to any point on line n?
a)48
b)50
c)60
d)75
e)100
I'll post the answer later. Thanks
I've corrected a typo: the equation of the line should be y = (4/3)x - 100.
The x-intercept of a line occurs when y=0.
Substituting y=0 into y = (4/3)x - 100, we get:
0 = (4/3)x - 100
x = 75.
Thus, the x-intercept of y = (4/3)x - 100 is (75,0).
DRAW the figure:
The SHORTEST DISTANCE between a point and a line must form a RIGHT ANGLE with the line.
Thus:
d = the shortest distance between the origin and y = (4/3)x - 100.
∆ABC is a multiple of a 3-4-5 triangle:
25*(3:4:5) = 75
125.
Thus, BC = 125.
Any side of a triangle can be considered the base.
Each base has a corresponding height.
A = 1/2(bh).
Since the area must be the same no matter which base and height are used, bh must always yield the same product.
In the triangle above:
If AB=75 is considered the base, the corresponding height is AC=100.
If BC=125 is considered the base, the corresponding height is d.
Since bh must yield the same product in each case, we get:
75*100 = 125d
d = 60.
The correct answer is
C.
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