What is the shortest distance between two points?
494502
This question is answered very well in solid geometry.\n\nOn a plane, it's a straight line.\n\nOn the surface of a sphere, it's a curved-line called a great circle.\n\nIn space, considering the curvature caused by the masses of any nearby bodies between you and the destination point, it may be a complex three-dimensional curve.
893759
Is a line perpendicular to it. The proof is easy.\nDraw a line not perpendicular to the straight line.\nCall this line L1.  Now draw a line perpendicular to the straight\nline. Call it L2. Note that you have a rt triangle with  sides made of L1 and a side from the intersection of L1 and the original line\nto the intersection of L2 and the original line and a hypotenuse which is L2. That makes L2 longer than L1 . So the shortest distance is necessarily perpendicular.
500659
9,047 miles.\n\nCity-Data provides the coordinates for Bushnell as 40.55 N, Longitude: 90.51 W.\n\nUsing the ‘Haversine’ formula - the shortest distance over the earth’s surface – and the South Pole at 90.00S, 0.00W, one gets 9,047 miles.
846254
Using University of Texas at Austin as a starting point and Juneau, Alaska as a ending point the shortest distance is 2231.5 miles with a travel time of 69 hours and 44 minutes hope this helps.
263422
Distance=rate*time\n\nJust plug in what you know and solve for what you're missing.
172928
To find the distance between two points:\n\nSubtract the two first coordinates and square this answer (multiply it by itself)\n\nThen subtract the two second coordinates and square this answer\n\nAdd the two squared answers and do the square root of this sum\n\nThat's the distance\n\nSo, for (3,-2) and (-2, 10)...\n\n3 - -2 = 5, 5 squared is 25\n\n-2 - 10 is -12 squared is 144\n\n144+25=169\n\nsqrt (169) = 13\n\nSo the distance is 13
700857
The shortest distance for a house to be built away would be for the house to be touching the tower. The safest realistic distance would be exactly half way around the world for the tower.
418614
This problem can be described by:\n\ndistance from A to pt = distance from B to pt\ndistance from B to pt = distance from C to pt \n\nsqrt( (x-11)^2 + (y-1)^2 ) = sqrt( (x-3)^2 + (y-6)^2 )\nsqrt( (x-3)^2 + (y-6)^2  ) = sqrt( (x-3)^2 + (y-4)^2 )\n\n\n(x-11)^2 + (y-1)^2 = (x-3)^2 + (y-6)^2\n(x-3)^2 + (y-6)^2  = (x-3)^2 + (y-4)^2\nI think x=87/16 , y=1 is a solution
710039
A line of best fits is a line that has the shortest distance between a set of data points.  This is usually used to make a generally complicated function easy to model since you would be using a linear model.  Generally, a good linear model would be to use a least squares approximation.  This minimizes the total vertical distance between all points on a scattered data plot.
781250
take a look at Attu Island, the westernmost island in the Aleutian Island chain off the southern coast of Alaska.  Measure the distance from there to Hokkaido prefecture, in northern Japan.  I believe you will find that is the shortest point between the two countries, clocking in at roughly 1300 miles or so.
749635
22 or 23 miles at the narrowest.\nD.
255863
About 4 to 20 minutes.\nThe distance between them can fluctuate between 0,5 to 2,5 AU.\nAn AU = the distance between Earth and  the Sun.
1079894
The basic definition of a parabola states that it is the locus of points that are equidistant from a given point (the focus), and a line (the directrix). Therefore, we have to find two distances:\n\nPoint-to-Point: d1 = sqrt( (x-11)^2 + (y+7)^2 )\nPoint-to-Line: d2 = abs( x-5 ) / sqrt (1^2) = (x - 5)\n\nThen, make the two distances equal, d1 = d2:\n(x-11)^2 + (y+7)^2 = (x-5)^2\n........simplifying........\ny^2 + 14y + 49 - 12x + 96 = 0\n\n(y + 7)^2 = 12*(x - 8)\n\nThis is the equation for our parabola.
798910
We know that the distance betwen two points is {(sqrt)(x1-x2)^2+(ya-y2)^2}\nBy the problem\n{(sqrt)(2+10)^2+(y-13)^2=13\n{(sqrt)(144+y^2-26y+169=13\n144+y^2-26y+169=169     [squaring both sides}\ny^2-26y+144=0\n(y-18)(y-8)=0      [factorising y^2-26y+144]\ntherefore y=18 or 8
352179
hmm... i'm not sure but i have decreased the distance between two objects!
1147518
distance between point A nad point B
252742
I believe the bounds are where the numbers are deviated but still close. Say, in the problem, 11 cm is measured to the nearest centimeter. So, it may not be 11cm. It could be 10.6 cm, 11.3 cm, or even 10.51294803 cm. But they'll all be 11cm in the measurement. \n\nSo for the question, if it's asking for the minimum possible area:\nLet l be length and w be breadth. \n10.5 <= l < 11.5\n8.5 <= w < 9.5\nThe lower bound would be composed of the shortest length and breadth. \nA = 10.5(8.5) = 89.25 cm^2