点 (4, 3) 到原点的距离是多少？
几何学无疑是数学领域最重要的分支之一。它的意义与算术和代数一样深刻，在我们的日常生活中以及在数学的技术性和复杂性中一样重要。几何，在日常生活中，基本上无处不在。它被应用于设计一个简单的茶水盒到手机或笔记本电脑到水箱，甚至是公共汽车、卡车，甚至是水坝。因此，任何占据空间并具有确定形状的东西都必须包含在几何学的范围内。在数学理论和问题中，几何的概念也被用来找出两个形状之间的距离、它们占据的空间、它们的大小和位置。
坐标平面
这种由两条线相交形成的平面，一条垂直，一条水平，在数学上称为坐标平面。它是一个二维平面，以垂直线为 y 轴，水平线为 x 轴。平面中两条线的交点称为原点，用 O 表示。匹配网格上的图形用于检测点。坐标平面可用于绘制点、线等。它充当图表，并产生从一个点到另一个点的精确方向。
坐标
坐标是一组两个值，它们在坐标平面网格（更好地称为坐标平面）上定位选定点。坐标平面内的点通过其有序对 (x, y) 已知，写在括号中，就像 X 坐标和 Y 坐标一样。这些坐标通常为正、零或负，具体取决于它们在各自象限内的位置。
不同象限中的坐标符号
坐标平面分为 x 轴和 y 轴的 4 个象限。第一个象限是最右上的一个，其中 x 和 y 坐标都是正数；第二个象限位于第一个象限的左侧，其中 x 坐标为正，y 坐标为负；第三象限位于第二象限正下方，x 坐标为负，y 坐标为正；第四象限位于第一象限的正下方和第三象限的右侧，其中 x 和 y 坐标均为负值。
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距离公式
简单来说，距离是对两个事物/对象/点相距多远的量化。很明显，距离公式将是一个数学方程，用于在给定坐标的情况下找出两个对象/点之间的距离。需要注意的是，所讨论的点不必属于同一象限。在数学中，距离公式专门用于坐标系中，借助坐标系来求出坐标平面上两点之间的距离，因此在几何学领域具有重要意义。
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为简单起见，假设在一个坐标平面上有两个点 A 和 B，第一象限。点 A 的坐标是 (a,b)，B 是 (p,q)。点 A 和 B 之间的距离（用 AB 表示）应由下式给出：
AB = _from_the_origin?_2.jpg "Rendered by QuickLaTeX.com")
距离公式的推导
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The formula is a direct application of the Pythagorean Theorem. The right triangle ASJ, with its hypotenuse AB would represent the required distance between the two points.
By Pythagoras Theorem,
AB2 = AJ2 + BJ2
= (a-p)2+(b-q)2
AB = _from_the_origin?_4.jpg "Rendered by QuickLaTeX.com")
点到原点的距离
Let the coordinates of the point be (x,y). The coordinates of origin are (0,0).
Using distance formula, we have:
d = _from_the_origin?_5.jpg "Rendered by QuickLaTeX.com")
Distance of a point from the origin = _from_the_origin?_6.jpg "Rendered by QuickLaTeX.com")
点 (4, 3) 到原点的距离是多少？
解决方案：
We know, distance of a point from the origin = _from_the_origin?_7.jpg "Rendered by QuickLaTeX.com")
Hence, required distance = _from_the_origin?_8.jpg "Rendered by QuickLaTeX.com")
= _from_the_origin?_9.jpg "Rendered by QuickLaTeX.com")
= 5
Thus, the distance of the point (4, 3) from the origin is 5 units.
类似问题
问题1.计算点（-100,0）到原点的距离。
解决方案：
We know, distance of a point from the origin = _from_the_origin?_10.jpg "Rendered by QuickLaTeX.com")
Hence, required distance = _from_the_origin?_11.jpg "Rendered by QuickLaTeX.com")
= _from_the_origin?_12.jpg "Rendered by QuickLaTeX.com")
= 100
Thus, the distance of the point (-100,0) from the origin is 100 units.
问题 2. 计算点 (9,5) 到 (4,5) 的距离。
解决方案：
Using distance formula, the distance between A(a,b) and B(p,q) is
AB = _from_the_origin?_13.jpg "Rendered by QuickLaTeX.com")
Hence required distance = _from_the_origin?_14.jpg "Rendered by QuickLaTeX.com")
= _from_the_origin?_15.jpg "Rendered by QuickLaTeX.com")
= 5
Thus, the distance of the point (9,5) from (4,5) from the origin is 5 units.
问题 3. 计算点 (8,6) 到原点的距离。
解决方案：
We know, distance of a point from the origin = _from_the_origin?_16.jpg "Rendered by QuickLaTeX.com")
Hence, required distance = _from_the_origin?_17.jpg "Rendered by QuickLaTeX.com")
= _from_the_origin?_18.jpg "Rendered by QuickLaTeX.com")
= 10
Thus, the distance of the point (8,6) from the origin is 10 units.
问题4.计算(5,12)点到原点的距离。
解决方案：
We know, distance of a point from the origin = _from_the_origin?_19.jpg "Rendered by QuickLaTeX.com")
Hence, required distance = _from_the_origin?_20.jpg "Rendered by QuickLaTeX.com")
= _from_the_origin?_21.jpg "Rendered by QuickLaTeX.com")
= 13
Thus, the distance of the point (5,12) from the origin is 13 units.
问题 5. 计算点 (3,5) 到 (1,2) 的距离。
解决方案：
Using distance formula, the distance between A(a,b) and B(p,q) is
AB = _from_the_origin?_22.jpg "Rendered by QuickLaTeX.com")
Hence required distance = _from_the_origin?_23.jpg "Rendered by QuickLaTeX.com")
= _from_the_origin?_24.jpg "Rendered by QuickLaTeX.com")
Thus, the distance of the point (3,5) from (1,2) from the origin is _from_the_origin?_25.jpg "Rendered by QuickLaTeX.com")
units.