I found this one to be interesting. Took me 8 mins to solve and still had to semi-guess (thankfully correctly). A shorter solution is a clever one.
What is the least possible distance between a point on the circle X^2+y^2 = 1 and a point on the line y=0.75x-3
A) 1.4
B) Sqrt(2)
c) 1.7
d) Sqrt(3)
e) 2.0
OA: A
Interesting geometry/coordinate plain question
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- logitech
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X^2+y^2 = 1 is a circle with radius 1 around the center of X,Y planeadilka wrote:I found this one to be interesting. Took me 8 mins to solve and still had to semi-guess (thankfully correctly). A shorter solution is a clever one.
What is the least possible distance between a point on the circle X^2+y^2 = 1 and a point on the line y=0.75x-3
A) 1.4
B) Sqrt(2)
c) 1.7
d) Sqrt(3)
e) 2.0
OA: A
y=0.75x-3 for x=0, y =-3 and for y=0 x =4 So it forms 3,4,5 right triangle.
The shortest line should be perpendicular to the line , that goes to the center of the circle , so it is actually the HEIGHT of the triangle
The area of the triangle can be written in two forms to find this height
(3x4)/2 = (5xh)/2 so this gives us 12/5
well 1 is the radius , so the distance is 12/5 - 1 = 7/5 = 1.4.
It is long to explain but I solved this under a minute.
LGTCH
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- adilka
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Great solution. That's exactly how it was explained. I failed to make a connection between the height and the area, so was solving for the height in a different way.
Great job, logitech
Great job, logitech