find the distance between (7,2), (0,-7) round to the nearest tenth

Question

find the distance between (7,2), (0,-7) round to the nearest tenth

Answer 1

It is helpful to realize that the distance formula is simply the Pythagorean theorem applied to a two-dimesional x-y coordinate system.

The x- and y-dimensions are perpendicular to one another. So calculating distances involves horizontal and vertical distances, and that invites the use of this theorem.

(Recall that the Pythagorean theorem is a² + b² = c², where a and b are the lengths of the legs and c is the length of the hypotenuse.)

The x-distance represents the length of one of the legs. So, calculate the x-distance by subtracting the x-values from one another: x₁ - x₂ and then squaring the result. In this case, 7 - 0 = 7, and when squared we have 49.

The y-distance represents the length of the other leg. Similar to what we did for the x-values, we need to subtract the y-values from one another. In this case, we have 2 - (-7) = 2 + 7 = 9, and when squared we have 81.

Note that we are working with ordered pairs. This term is used to reinforce the fact that x is always first and y is always second. If you have any problem rembering this, use this to help you: "x is before y in the alphabet, and x is before y in algebra". (Mathematicians like to use the most concise notation possible.)

Finally, add the squared distances and then take the square root. 49 + 81 = 130, and the square root of 130 is 11.402 to 3 decimal places of accuracy. When rounded to the nearest tenth, this is 11.4

Using these steps will make it easier to understand and remember the distance formula, in my experience.

Note that which way you subtract the values does not make a difference because squaring the result always yields non-negative values. You do have to keep the x-values separate from the y-values, but this formula is much harder to make a mistake with than, for instance, the slope formula.

Also, many math teachers prefer that you leave the value as a radical, since that is an exact value.

In addition, you will soon learn how to reduce radicals to their "standard" value. √130 cannot be reduced. But this is often the last step when a reduction is possible, other than checking your work. The right answer to the wrong problem has no useful value.

Answer 2

D=√(x₂-x₁)²+(y₂-y₁)²

^{To find the distance formula between two points we utilize this formula to look at the difference of x's and y's by computing and taking the square root.}

^{For example between (7,2) and (0,-7) let identify our variables. x}₁=7 and y₁=2 because there the coordinates of the first point. X₂=0 and Y₂=-7 are the coordinates of the second point. So after we identify then substitute into the formula to find the distance.

d=√(0-7)²+(-7-2)²=√(-7)²+(-9)²=√49+81=√130 which is then approx. 11.4 rounded to nearest tenth

Any further questions please let me know and hope this work assists when finding the distance between two points.