Q&A for How to Find the Distance Between Two Points

Subtract 3 from 8 since both are at 4 on the y axis. So distance is: 8-3=5.

This is an ambiguous question. I will assume you mean the shortest distance. Then, your second point will be (7,0) because the line that goes through (7,0) and (7,-2) is perpendicular to the x-axis. So your answer is 2.

Using the distance formula shown in the above article, find the horizontal distance between the two points by subtracting (-8) from 2, which is 10. Then find the vertical distance between the points by subtracting 12 from 3, which is -9. We then add together the squares of those two distances: 3² + (-9)² = 9 + 81 = 90. Find the square root of that sum: √90 = 9.49. That's the distance (in "units") between the two points.

It's not likely you will use this technique in a real-life application. It is a way to practice using graphs and the Pythagorean theorem.

You still fill in the formula the same way, remembering that the negative signs are part of the formula. The negative numbers squared become positive, so there should not be any problem in the end.

The x-coordinate of the midpoint is half the distance between 45 and 66: 66 - 45 = 21. Half of 21 is 10½. Add 10½ to 45 to get the midpoint's x-coordinate, 55½. The y-coordinate of the midpoint is half the distance between 972 and 191: 972 - 191 = 781. Half of 781 is 390½. Add 390½ to 191 to get the midpoint's y-coordinate, 581½. So the midpoint is (55½, 581½).

Because all you care about is distance, not direction, you can subtract in either order. You just want to know how far apart the two points are, and subtracting in either direction will tell you. That's true of both the horizontal and vertical directions.

Let (x_1, y_1) = (4,6) and (x_2, y_2) = (-5,8). The distance formula is sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2). Simply plug in to the formula, and you obtain sqrt(85).

The distance formula is sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2). 3-(-4)=7-5-2=-7 (7)^2=49 (-7)^2=49 sqrt(49+49)=9.8.

The distance formula is sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2). 7= sqrt((x-5)^2 + (4-2)^2)....> Square both side....>49=(x-5)^2 + (4-2)^2 .=>49=(x-5)^2+4=>49-4=(x-5)^2 =>45=(x-5)^2=>sqrt(45)=(x-5)=>x=6.7-5=>x=1.7

The distance formula shown above does not require graphing or counting.

If the two points are defined only as being on a coordinate plane, the distance formula is the only way to find the distance between them. If they are defined differently, however, (as the vertices of a geometrical figure, for instance, or as the center of a circle and a point on that circle's circumference) there would be several other ways to find the distance between them.

You don't. Distance is a measurement of the space between two points only.

On a number line there is a distance of 6 between -2 and +4.

It's "hard" because it requires a certain kind of mental maneuvering which can be learned and practiced but which does not come naturally to many people. Others who are mentally "wired" in a particular way find math to be interesting and even fun.

Subtracting a negative number is the same as adding a positive number. For example, 5 - (-4) = 5 + 4 = 9. This means that there are 9 units of distance between 5 and -4.

The origin is (0,0), so the distance from there to (6,7) is √(6² + 7²) = √(36 + 49) = √85 = 9.22.

No. That formula is as short and simple as it gets.

Yes, exactly the same, although the decimal makes it slightly more difficult.

Yes, that answer is correct.