what is the distance between (4,0)(-9,0)?

Question

I need help understanding how to work these types of problems out. Can someone help?

Answer 1

This is simply on the y xis so the distance is
4 - (-9) = 13 units.

On a more genral note if two points are (x,y) and (m,n) then distance between them is
sq root( (x-m)^2 +(y-n)^2)

Answer 2

the distance is 13. since both points are on the x-axis, just subtract 4 from -9; this would become 4+9 or 13.

if the two points don't share any x or y coordinates, square the difference of the x-coordinates and add it to the square of the y-coordinates. this would be the square of the length of that segment.

it's like the Pythagorean theorem, where the segment formed by the two points is the hypotenuse of a triangle.

for example, if you had (2,3) and (5,7), the length would be 5. 5-2 is 3 and 7-3 is 4; that makes a 3-4-5 right triangle. not all problems would work out so neatly, but you can still use the Pythagorean theorem.

Answer 3

Think of the points as those of the ends of a right triangle. Then with the origin as the vertex opposite the hypotenuse, you can apply the Pythagorean theorem:
Distance = sqr[(x2-x1)^2 + (y2-y1)^2] where
x1,y1 = 4,0
x2,y2 = -9,0
So distance = sqr[(-9-4)^2 + (0-0)^2] = sqr[13^2] = 13

Answer 4

the distance between two points (x1,y1) and (x2,y2) is
sqrt((x1 - x2)^2 + (y1 - y2)^2)
since x1 and x2 are both zero in your question, the answer is simply y1 - y2 = 4 - (-9) = 13

note that the method of calculating the distance between two points will change for different coordinate systems (such as polar coordinates)

{sqrt == square root}