 # High school geometry questions and answers

Recent questions in Geometry Adrien Jordan 2022-09-27

### Minkowski difference of two convex polygonsI just want to make sure that the following algorithm is correct for computing the Minkowski difference of two shapes A,B:Where CH(S) is the convex hull of the set S and a,b are the vertices of the two polygons. Sara Fleming 2022-09-27

### How to recognize what type of probability distribution to use in solving probability problems?Bernoulli's, Binomial, Geometric, Hypergeometric, Negative binomial, Poisson's, Uniform, Exponential, Normal, Gamma, Beta, Chi square, Student's distribution.I would like to know how and when to use each of these distributions when solving problems in probability. If possible, make analogy with combinatorics (when we use permutations, variations and combinations). mydaruma25 2022-09-27

### A certain discrete random variable has probability generating function: ${\pi }_{x}\left(q\right)=\frac{1}{3}\frac{2+q}{2-q}$Compute . (Hint: the formula for summing a geometric series will help you expand the denominator)." Wevybrearttexcl 2022-09-26

### Distance between (-2,1,3) and (-1,4,-2)? Medenovgj 2022-09-26

### What is the distance between (3,-14,15) and (12,-21,16)? koraby2bc 2022-09-26

### Distance between (11,-13,-5) and (9,-14,4)? Kody Whitaker 2022-09-26

### Determine the coordinates of the unknown vertex or vertices of each figure below. Use variables if necessary.I'm not sure how to find $C$ and $E$.  mundocromadomg 2022-09-26

### What is the distance between (-11,-11) and (21,-22)? Averi Fields 2022-09-26

### Let ABC be a triangle and $\mathrm{\Omega }$ be its circumcircle, the internal bisectors of angles A, B, C intersect $\mathrm{\Omega }$ at ${A}_{1},{B}_{1},{C}_{1}$. The internal bisectors of ${A}_{1},{B}_{1},{C}_{1}$ intersect Omega ${A}_{2},{B}_{2},{C}_{2}$. If the smallest angle of $\mathrm{△}ABC$ is 40 degrees, find the smallest angle of $\mathrm{△}{A}_{2}{B}_{2}{C}_{2}$. Marcus Bass 2022-09-26

### Geometric probabilityInside a square of side 2 units , five points are marked at random. What is the probability that there are at least two points such that the distance between them is at most $\sqrt{2}$ units? Medenovgj 2022-09-26

### Let $Q\left(z\right)=\left(z-{\alpha }_{1}\right)\cdots \left(z-{\alpha }_{n}\right)$ be a polynomial of degree $>1$ with distinct roots outside the real line.We have$\sum _{j=1}^{n}\frac{1}{{Q}^{\prime }\left({\alpha }_{j}\right)}=0.$Do we have a proof relying on rudimentary techniques? gaby131o 2022-09-25

### Probability of Observing N particles in a given volume?I'm having an issue with a probability problem concerning solutions.Assume there is an "observational region" in a dilute solution with a volume V, and as solutes move across its boundary, the number N of solute molecules inside the observation region fluctuates.Divide V into M regions of volume v each with n particles. The solution is dilute enough that $n=0$ or 1 (there is no v with more than one particle of solute), and each cell is occupied ($n=1$) with probability $p=\left({\rho }_{0}\right)v$.If W(N) is the number of configurations of the observation volume when N solutes are present, what is the probability P(N) of observing a given value of N, in terms of p,W(N),M, and N.I know the probability $P\left({n}_{1},{n}_{2},\dots ,{n}_{M}\right)$ of finding the system in a particular configuration in the observation volume is $p\left(N\right)={p}^{N}\left(1-p{\right)}^{M-N},$, (Bernoulli Distribution), and since there are N particles in M spaces then the maximum number of configurations is $\frac{M!}{\left(N!\left(M-N\right)!\right)}$I'm not sure where to go from here. Harrison Mills 2022-09-25

### Distance between (3,-1,1) and (4,1,-3)? tarjetaroja2t 2022-09-25

### Gram Determinant equals volume?I have been trying to solve this problem of finding the 'n-volume' of a paralleletope spanned by m vectors, where clearly $m\le n$. In general, for computational purposes, what I have managed to do is define volume as the product of absolute values of vectors obtained by gram-schmidt orthogonalizationn. (Makes sense right? That's the natural interpretation when we say volume)I had to do two things, firstly to show that this definition of volume is a well defined one (i.e. any set of orthogonal vectors obtained by the process will give the same volume), and secondly to find a quick way to do this. I managed to prove the first one by induction, but the second part is a little bit of a problem. I managed to obtain formulae for small dimensions as 2,3 or even 4 but this process is impractical for any bigger dimensions as the substitutions for smaller dimensions into the formula for the next dimension becomes exponentially complicatedHow does one prove that the gram determinant is equal to the volume of a paralleletope spanned by a set of vectors? Melina Barber 2022-09-25

### Suppose we have the following:Can this be proven without making assumptions for conditional or indirect proofs? deiluefniwf 2022-09-25

### You have a quadrilateral ABCD. I want to find all the points x inside ABCD such that$angle\left(A,x,B\right)=angle\left(C,x,D\right)$Is there a known formula that gives these points ? basaltico00 2022-09-25

### How can we draw a triangle give one of its vertex and the orthocentre and circumcentre? kennadiceKesezt 2022-09-25

### Show that the equations to the straight lines passing through the point $\left(3,-2\right)$ and inclined at ${60}^{\circ }$ to the line $\sqrt{3}x+y=1$ are $y+2=0$ and $y-\sqrt{3}x+2+3\sqrt{3}=0$ madeeha1d8 2022-09-25
### Triangles : isoceles and angles inside with other triangleWe have one main isoceles and another one inside of it. I have attached here a diagram, and we wish to find the angle in red: The labels blue means : lengths $PQ=QR$ The label green means : lengths $QS=QT$. The given angle $PQS=24$ (deg)We wish to find angle in red, angle RST. Darius Miles 2022-09-25