Example Question - plane geometry problem
Here are examples of questions we've helped users solve.
Solving a Plane Geometry Problem using Pythagorean Theorem
这个问题是一个利用勾股定理来解决的平面几何问题。首先，我们有一个直角三角形ABC，其中∠ACB是直角。 已知两条边： AB = 2； AC = 2√3。 我们需要计算第三边BC的长度。 根据勾股定理，直角三角形的斜边（即此处的BC）的平方等于两条直角边的平方和，即： BC² = AB² + AC²。 带入已知数值： BC² = 2² + (2√3)² BC² = 4 + 4*3 BC² = 4 + 12 BC² = 16。 现在我们要找BC的长度，所以我们取平方根： BC = √16 BC = 4。 因此，BC的长度是4。在提供的选项中没有直接为4的选项。所以可能图片问题选择题部分有笔误或看错数字。在标准数学问题条件下，BC的正确答案应该是4。
Intersection of Two Lines in a Plane
The image contains a problem written in German, which translates to "Examine the intersection behavior of the given two lines in the plane" for the equations: 1. \(6x_1 + 3x_2 = 10\) 2. \(7x_1 - 2x_2 = -1\) To find out if the lines intersect, we can use these two equations to solve for \(x_1\) and \(x_2\). This is a system of linear equations that we can solve using various methods such as substitution, elimination, or matrix methods. I will use the elimination method. First, write the equations in standard form: \(6x_1 + 3x_2 = 10\) (Equation 1) \(7x_1 - 2x_2 = -1\) (Equation 2) Our goal is to eliminate one of the variables. To do this, we can multiply the first equation by 2 and the second equation by 3 to make the coefficients of \(x_2\) match: \(12x_1 + 6x_2 = 20\) (Equation 3, multiplied by 2) \(21x_1 - 6x_2 = -3\) (Equation 4, multiplied by 3) Next, add the two equations together to eliminate \(x_2\): \(12x_1 + 6x_2 + 21x_1 - 6x_2 = 20 - 3\) \(33x_1 = 17\) Solve for \(x_1\): \(x_1 = \frac{17}{33}\) \(x_1 = \frac{17}{33} * \frac{3}{3} = \frac{51}{99}\) \(x_1 = \frac{1}{2}\) Now that we have the value for \(x_1\), we can substitute it back into one of the original equations to find \(x_2\). Let's use Equation 1: \(6(\frac{1}{2}) + 3x_2 = 10\) \(3 + 3x_2 = 10\) \(3x_2 = 10 - 3\) \(3x_2 = 7\) Solve for \(x_2\): \(x_2 = \frac{7}{3}\) So the solution to the system of equations, which represents the intersection point of the two lines, is \(x_1 = \frac{1}{2}\), \(x_2 = \frac{7}{3}\). The two lines intersect at this point.
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