大家好，今天给大家分享两点间距离公式是什么时候学的，一起来看看吧。

The distance formula is an algebraic expression that gives the shortest distance between two points in a two-dimensional space.

距离公式是一个代数表达式，它给出了二维空间中两点之间的短距离。

You&39;t too hard, but on the second page, you see a graph with two little dots on it labeled &34; and &34; And they&34;Find the distance between these points.&39;t panic — you don&39;re looking for is fairly straightforward and has ties to one of the most useful and famous concepts in all of mathematics: the Pythagorean theorem.

不要惊慌——你甚至不需要一个距离计算器来解决这个问题。你要找的距离公式是相当直接的，它与数学中有用、著名的一个概念有关:勾股定理。

Contents 内容

勾股定理与距离公式有关

The Pythagorean theorem was named for the Greek philosopher Pythagoras. But he can&39;ve got a couple of things to unpack here. A right triangle, also known as a right-angled triangle, is one that contains one 90-degree angle, also known as a right angle. The longest line on a right triangle is called the hypotenuse. (This is the line situated on the opposite side of the right angle.)

我们还有一些东西要整理。直角三角形，也叫直角三角形，是包含一个90度角的三角形，也叫直角。直角三角形中长的一条线叫做斜边。(这是直角的对边。)

Now as we all know, a triangle may have three sides, but a square&39;ll end up with three individual squares.

想象一下，取一个直角三角形的斜边把它变成一个新正方形的四条线中的一条。然后对原来三角形的另外两条边做同样的事情。你会得到三个独立的方块。

As the Pythagorean theorem points out, the square you just made with the hypotenuse will have the same area as the other two squares put together. If the hypotenuse was labeled &34; and those other line segments were labeled &34; and &34; then we could express that idea like so:

正如毕达哥拉斯定理所指出的，你刚刚用斜边做的正方形的面积与其他两个正方形加起来的面积相等。如果斜边标注为c，其他线段标注为a和b，那么我们可以这样表达:

The Pythagorean theorem says a2 b2 = c2. The distance formula is derived by using the Pythagorean theorem.

毕达哥拉斯定理（勾股定理）说a2 b2 = c2。利用毕达哥拉斯定理推导了距离公式。

距离公式与点坐标平面

When most people hear the word &34; they&39;s not-so-relaxing vacation where the y-axis is labeled &34; and the x-axis is labeled &34;

这条垂直线被称为y轴，它的水平对应物是x轴。这两条线一起用数据讲述一个故事。看看漫画家豪尔赫·查姆(Jorge Cham)画的这张关于某人不太放松的假期的幽默图表，y轴被标记为“压力”，x轴被标记为“时间”。

In order to make sense of where one point rests on your graph, you need to measure where it falls along the two dimensions (the x-axis and the y-axis). These are known as the point&39;ll use the distance formula to measure the straight line segment connecting the two points.

为了理解一个点在图形上的位置，需要测量它在两个维度(x轴和y轴)上的位置。这些被称为点的坐标。在计算它们之间的距离之前，你需要找到**个点和第二个点的坐标。你将使用距离公式来测量连接这两点的直线段。

如何推导距离公式

Enough preamble. The question you want answered is how to find the distance between two points on a graph (i.e., two sets of two coordinates).

足够的开场白。你想要回答的问题是如何找到图上两点之间的距离(即，两个坐标的两个**)。

The first point and second point on your graph will each have an x coordinate and a y coordinate. You can calculate the shortest distance between these two points by using the Euclidean distance formula, which is a Pythagorean theorem-related algebraic expression. Here it is, folks:

图中的**个点和第二个点都有一个x坐标和一个y坐标。您可以通过使用欧几里得距离公式计算这两点之间的短距离，这是一个与勾股定理相关的代数表达式。下面就是，各位:

D = √(x2-x1)2 (y2-y1)2

Note that &34; means &34; As for x2 and x1, they refer to the x coordinates of Point 2 and Point 1, respectively. Same goes for y2 and y1, except those are the two y coordinates.

注意“D”的意思是“距离”。其中x2和x1分别指点2和点1的x坐标。y2和y1也一样，只是它们是两个y坐标。

So to calculate the distance, our first step is to subtract x1 from x2. Then we have to multiply the resulting number by itself (or, in other words, &34; that number). After that, we must subtract y1 from y2 and then square the answer we get from doing so.

为了计算距离，**步是用x2减去x1。然后我们必须将得到的数字乘以自身(或者，换句话说，“平方”这个数字)。之后，我们必须用y2减去y1，然后平方得到的结果。

This will leave us with two numbers we must add together. Then finally, take that number and find its square root. And that square root, ladies and gentlemen, is our distance.

这就剩下两个数字，我们必须把它们相加。后，求出这个数的平方根。这个平方根，女士们先生们，就是我们的距离。

计算两点之间的距离

OK, so let&39;s got an x coordinate of 9 and a y coordinate of 13.

假设点1的x坐标是2 y坐标是5。假设点2的x坐标是9 y坐标是13。

Plug those values into the handy dandy formula and you get this:

把这些值代入这个简单的公式，你会得到这个:

D = √(9-2)2 (13-5)2

What&39;re left with this:

现在我们就剩下这个了:

D = √72 82

If you &34; 7 — as in, multiply the number by itself — you end up with 49. As for 8 squared that works out to 64. Let&39;re cooking. Add 49 and 64 and you get 113.

现在我们开始做饭。49加64得113。

D = √113

What's the square root of 113? The answer is 10.63, so therefore:

113的平方根是多少?答案是10.63，因此:

D = 10.63

Go forth and ace that pop quiz!

去做突击测验吧!

以上就是两点间距离公式是什么时候学的的内容分享，希望对大家有用。