On a grid, what is the distance between two points located at (2,1) and (14,6)?

Question

A. 13
B. 12
C. 17.46
D. 5

Answer 1

its 13...

Answer 2

Okay think of this question with triangles, specifically the hypotenuse formula A^2 + B^2 = C^2.
Okay, so imagine a line going to the right from the point 2,1 and a point coming down from 14,6, and then a line going between 2,1 and 14,6. It looks like a right triangle now!

So now you find the length of the two sides. 14-2 will give you 12, so the length of the triangle on the x-axis part is 12. 6-1 is five, so the triangle is 5 units tall. 12^2 + 5^2 is 144 +25 which = 169. Now the root of that is 13.

The formula for all this is D^2 = (x - x)^2 + (y-y)^2. (I can't figure out how to write it, but you say it like x-two minus x-one. It's the more x further to the right minus the x further to the left. Same as the y's, but taller y minus shorter y) So you plug the numbers in:
d^2 = (14 - 2)^2 + (6-1)^2
d^2 = 169
square root both sides
d= 13

Answer 3

The X distance is 14 - 2 which is 12. The Y distance is 6 - 1 which is 5. So the total distance is given by Pythagoras's theorem. D² = 12² + 5²

Work it out.

Answer 4

You need to specify the metic on the set you are working on. For example:

A = (2, 1)
B = (14, 6)

In R2, the Eucledian norm gives

d (A, B) = sqrt( (14 - 2) ^ 2 + (6 - 1) ^ 2) = sqrt(13^2) = 13

However using R_Infinity we get the norm

d (A, B) = max ( (14 - 2), (6 - 1)) = 12

Thus both A and B in your answers are correct!!! Sweet!!!

Answer 5

The distance formula is

d = sqrt( (x2 - x1)^2 + (y2 - y1)^2 )

Plugging in (x1, y1) = (2, 1) and (x2, y2) = (14, 6), we get

d = sqrt( (14 - 2)^2 + (6 - 1)^2 )
d = sqrt( 12^2 + 5^2 )
d = sqrt(144 + 25)
d = sqrt(169) = 13

Answer 6

Use the Pythagorean Theorem, a^2 + b^2 = c^2,
where the length of one leg is the difference in the x values and the length of the other leg is the difference in the y values.

Answer 7

DISTANCE FORMULA

d = √(x2-x1)² + (y2-y1)
d = √(2-14)² + (1-6)
d= √(-12)² + (-5)²
d= √144 + 25
d= √169
d= 13

Answer 8

distance between them=sqrt( (x1-x2)^2 +(y1- y2)^2 )
=sqrt(12^2 +5 ^2 )
=sqrt(144 +25)
=sqrt(169)
13.
so it should be A.

Answer 9

Use Pythagorean theorem. sqrt of the sum of the squares of the right angle sides, i.e., sqrt(delta_x^2 + delta_y^2)

Answer 10

A