# Questions tagged [plane-geometry]

Plane geometry is a subfield of Euclidean geometry, restricted to the flat two-dimensional space. Plane geometry studies shapes, ratios and relative locations of 2D figures which can be embedded into 2D plane.

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### What is the subspace with scalar equation $-2x_1+3x_2+x_3−x_4=0?$ A plane in $R_4$ or a hyperplane in $R_5?$ [closed]

Problem : The subspace with scalar equation $-2x_1+3x_2+x_3−x_4=0$ is a. a plane in $R_4$. b. a hyperplane in $R_5$. My Thought Process : I think since there are $4$ variables in scalar equation, ...
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### what makes some line to be a tangent line on to other Graph.

I learned tangent line as a concept associated with a circle. I thought to make a tangent line, it might have some specific point which is perpendicular to. as always did with circle did. But in the ...
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### Determining A Vector Through the Center of Multiple Points on a Sphere

I am working on a machine vision task that requires me to determine spin rate and spin axis of a moving ball. I have had some luck, and actually do have a solution but am looking for a more efficient ...
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### Find location and normal of a plane based on the relative intersection points from 3 lines

Here is an illustration of the problem I have 3 points in a 3d space, in my example the points are: (0, 0, 0), (26, 0, 0) and <...
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### Is this converse results of Varignon's theorem known?

The Varignon's Theorem on Quadrilateral is very well known results of Plane Geometry and we have find the Converse of this theorem on Quadrilateral and generalise this for 2n-sided convex irregular ...
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### A 2-dimensional bounded domain's boundary is connected iff the domain contains the interior of every enclosed closed Jordan curve

I'm looking for a detailed proof, or a reference to a detailed proof, of the following theorem. Let $G$ be a non-empty, bounded domain in the Euclidean plane $\mathbb{R}^2$. Then $G$'s boundary is ...
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### What's the measure of angle $PCB$ in the figure below?

For reference: In the interior of a triangle ABC, a point $P$ is marked in such a way that: $PC=BC$ and the measure of the angle $PAB$ is equal to the measure of the angle $PAC$ which is $17°$. ...
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### What's the measure of the angle $ACD$ im trapezoid below?

For reference: On a rectangular trapezoid $ABCD$ right at A and B. Mark a point $L$ on $AB$ such that: $CL=AL=AD$ and $AC=CD$, calculate the measure of angle $ACD$.(Answer:$30^o$) My progresss: Follow ...
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