0
votes
2answers
32 views

Splitting a segment with a ratio

I came across the homework question that I attempted to do. After looking at the answers, and getting it wrong I didn't understand why. I'm specifically lost at why we would get a fraction of 2/5 ...
0
votes
0answers
37 views

Apps for making geometric shapes [on hold]

Is there any apps for making geometric shapes? I need to make shapes like rhombus and equilateral triangles.
-1
votes
0answers
171 views

What is a bi-rhombus? [on hold]

Can anyone tell me what a bi-rhombus is? I need it for my school project.
3
votes
2answers
53 views

How can I find the volume of prism: $V = \frac{(a + b + c)Q}{3} $

In the book Handbook of Mathematics (I. N. Bronshtein, pg 194), we have without proof. If the bases of a triangular prism are not parallel (see figure) to each other we can calculate its volume by ...
1
vote
2answers
18 views

Side length of a square in a squared rectangle

I have a squared rectangle where I want to find the side length of a sub-square (for the record, consult the omniscient Google). Here's what I've already done. $$14 + 4 + x = \mathrm{height}.$$ ...
0
votes
3answers
37 views

distance from a point to line segment not it 's perpendicular line's distance

how to find distance between line and point in the picture ? what is the shortest distancing point in the line ? Note: distance between line and point means line segment,(the intersecting point ...
1
vote
1answer
39 views

Converge of an inversion to a mirrorring

I want to ask something about a mirroring and a inversion in $\mathbb{R}^n$. An inversion in a sphere with center $m$ and radius $\rho$ can be written as $$ v \ \longmapsto \ ...
0
votes
0answers
31 views

Trying to prove that two angles are congruent in a isosceles trapezoid

I was given this assignment to do the following. Write a paragraph proof for the following scenario. Given: KLMN is an isosceles trapezoid. Prove: ∠LKM is congruent to ∠MNL The thing is that I ...
0
votes
3answers
41 views

getting the slopes of the sides of an equilateral triangle given 2 points

I want to get the slopes of an equilateral triangle given the 2 vertices. Let's say they are (0, 0) and (5, 5). Graphing this would give 2 triangles forming a diamond. I tried to use distance formula ...
0
votes
2answers
37 views

How to find the third vertex of an isosceles triangle given 2 points.

This is the full problem: The points $A(5,1)$ and $B(-3,6)$ represent one of the equal sides of an isosceles triangle. Determine one of the possible points that would represent the third vertex of the ...
1
vote
2answers
41 views

Find the radius of four congruent circles inside a right triangle

Below is a homework assignment I'm working on, along with a correct method for solving it and what appears to be an incorrect method. I'm hoping someone could explain what is wrong with the second ...
1
vote
0answers
38 views

Tangent bundle is orientable

I am having some trouble finishing a proof that the tangent bundle of any manifold is orientable. What I've done so far is calculate the transition function between two standard charts on the bundle. ...
2
votes
2answers
54 views

Primary school math regarding circles [closed]

----------//-----------------------------------__________ Please see the figure below the question is in the ...
-1
votes
3answers
21 views

point on a line and distance from a point

I have point(x1,y1) and point(x2,y2) these are end point of line and point(m,n) is a point. How can i find Point(a,b) which lies on the line ,that is the shortest path from point(m,n) to the line
0
votes
1answer
15 views

How would I find the scale factor of a dilated figure on a coordinate plane?

The above question is pretty simple, and I used common sense to figure out that the coordinates (3, -7) is the answer, since it is the only viable spot. I was wondering how I would find the scale ...
0
votes
1answer
33 views

Circles and tangents

3 circles of radius 3 cm, 4cm, 5 cm touch each other externally at $A$, $B$, $C$. Tangents drawn at $A$, $B$, $C$ intersect at $P$. Find $ PA + PB + PC$ . Thanks. My thoughts and approach: ...
0
votes
2answers
24 views

Calculate the sum of triangle's medians squared if hypotenuse is 2

Given a right triangle with sides a,b and a hypotenuse c=2, calculate the sum of trianle's squared medians i.e. if medians are x,y, and z, calculate $x^2+y^2+z^2$ The only thing i thought of is ...
2
votes
3answers
66 views

Finding an area of a triangle inside of a triangle, given certain areas of other triangles, and area ratios.

I'm studying for the Waterloo Math Contest (Galois, Gr. 10) taking place in April of 2015 and I am preparing by looking at previous problems and solving them. This is question 4(c) on the 2010 Galois ...
3
votes
1answer
54 views

Distance to foci on an ellipse?

I am trying to prove that for the ellipse: $$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$$ the sum of the distances from the gernal point to the foci ( $(ae,0)$ and $(-ae,0)$ were $e$ is the eccentricity) is ...
1
vote
1answer
29 views

Doubt on locus of a median point

I'm learning about geometric locus and ain't had an good time, I'm struggling with this problem: By the way, any study resource on geometric locus is welcome! Given an segment $AB$ formed by points ...
0
votes
1answer
20 views

Maximize area of a rectangle between parabola and a line

I was given a task to maximize the area of a rectangle that can be inscribed between parabola $y=1-x^2$ and a line $y=0$ such that one side of the rectangle lies on the $x$ axis. My idea is to somehow ...
-1
votes
1answer
24 views

Distance from X&Y plane from an point.

All , Given an point in xy plane have to calculate distance from specified point in plane. Eg: Given an specific point : (-3,5) other Points in XY plane : (2,9) , (-2,7),(-3,-3) have to ...
-4
votes
1answer
64 views

I know the perimeter of the rectangle but not the area. How do I find the length and width?

The perimeter of the rectangle is 986. I don't know the area and I need to find the length and width. The problem states that the length is 199 ft more than the width. That is all the information that ...
1
vote
0answers
45 views

Point of division of line segments one is 3/4 as the other

The segment joining A(2,-4) and B(9,3) is divided into segments one which is three fourths as long as the other. Find the point of division nearer to B(9,3). I'll call the point of division as ...
1
vote
1answer
33 views

Finding the area of a triangle in terms of the radius of the excircle

Prove that the area of a triangle $ABC$ is $$\frac12 (b + c - a)r$$ where $r$ radius of the excircle opposite to $A$ and the rest of the symbols have their usual meaning. I started off with the ...
0
votes
0answers
33 views

What is “d.c.s” here?

The equation of the plane in "normal form" is $\displaystyle lx+my+nz=a$, where l,m,n are the $\underline{d.c.s}$ of the normal from the origin to the plane. What is "$\underline{d.c.s}$" here ?
0
votes
0answers
42 views

Center of circumscribed circle of a triangle

I've been given the parametric equations of the height, median and inner angle bisector through the point $A$ of a triangle $\triangle{ABC}$: $$ h: \begin{cases}x = 2 - s \\ y = 1 \\ z = -3 + 2s ...
1
vote
1answer
24 views

Find the equation of a plane that is perpendicular to another plane, parallel to a line and goes through a point

Find the equation of a plane which is perpendicular to the plane $$\pi_1\equiv x-3y-z+1=0,$$ parallel to a line $$l\equiv\frac{x - 2}{2} = \frac{y -3}{-3} = \frac{z}{1}$$ and goes through point $P ...
0
votes
0answers
34 views

Basic complex geometry: Reflexion by a line. Where does $ \overline{z}$ go?

Where does $ \overline{z}$ go in the end? Shouldn't the formula be $f(z)= w^2 \overline{z} +2isw$? Thanks in advance. Original link: ...
0
votes
1answer
28 views

Find the area of the smallest tangential trapezoid?

So, how do I find the area of the smallest trapeziod with inscribed circle? The only thing I know is the circle radius, which is $8$.
2
votes
1answer
59 views

maths question for level 2 maths essential skills.

In Seville, Sue sees some wall tiles that she would like for her kitchen. The big tile measures $20 \text{ cm}\times 20 \text{ cm}$. The small tile measures $10 \text{ cm}\times 10 \text{ cm}$. How ...
1
vote
1answer
81 views

A sphere is cut, surface areas are given, calculate the perimeter

So I've tried everything! I'm stuck with this problem for at least an hour... A sphere is divided in 2 sphere caps. One bigger and one smaller, of course. The surface area of one ($P_1$) is $16 cm^2$ ...
0
votes
0answers
12 views

Is this system solution for plane intersection possible?

I have na exercise that asks me to find the parametric equation of the line formed by the intersection of the two planes: $$\pi_1: X = (1,-2,0) + \lambda_1(1,0,-1) + \mu_1(0,0,-1) $$ $$\pi_2: X = ...
2
votes
2answers
73 views

Number of lines determined given a set of points

Consider the following set of points in the $x-y$ plane: $$A=\{ (a,b)|a,b \in \mathbb{Z} \ and \ |a|+|b|\le 2\}$$ How to find the number of straight lines which pass through at least 2 points in ...
0
votes
1answer
36 views

What is the theorem called that states that equal angles gives equal sides?

We have an isosceles triangle, what is the theorem called that states that the sides opposite it's congruent angles will have congruent lengths? Could someone also explain why this is.
1
vote
1answer
20 views

Given $E=\mathbb{R}^3$, let $f$ be an endomorphism of $E$ defined by the matrix $A=(a_{i,j})$ on the canonic basis. Let $v,w$ be two eigenvectors.

Given $E=\mathbb{R}^3$, let $f$ be an endomorphism of $E$ defined by the matrix $A=(a_{i,j})$ on the canonic basis. Let $v,w$ be two linearly independent eigenvectors. Give a plane that is invariant ...
1
vote
0answers
45 views

Linear Transformation of points [duplicate]

Could you help me solve this: For projective coordinate system on the line $l$ are given points $A (2,1)$, $B (1,1)$, $C (0,1)$, $A_1 (0,1)$, $B_1 (1,5)$ and $C_1 (2,1 )$. Find a linear transformation ...
1
vote
1answer
39 views

Help me prove congruency

i) $AX = BC$ (given) $AD = CY$ (given since $AX = CY = BC$ and $BC = AD$ in a parallelogram) $\widehat{DAX} = \widehat{YCB}$ (equal opp. angles in a parallelogram) Therefore $ADX$ and $CBY$ ...
0
votes
4answers
40 views

Showing that these two lines are parallel.

$$ \dfrac{x - 1}{2} = 2 - y = 5 - z \quad \text{and} \quad \dfrac{4 - x}{4} = \dfrac{3 + y}{2} = \dfrac{5 + z}{2}. $$ I was given this math problem as homework, and I have spent the past hour ...
0
votes
2answers
35 views

How do i solve this?

Which of the following would result from multiplying each side of the polygon by a ratio of $\frac{1}{2}$? The final area is $24\text{ km}^2$ The final perimeter is $12\text{ km}$ The final area ...
1
vote
1answer
49 views

Griffiths Electrodynamics Example 1.8 - Calculating Volume Integral

In Example 1.8 in the electrodynamics textbook by Griffiths, he calculates the volume integral over a prism. The prism is formed of two triangles in the xy plane, with sides $x=0$ to $x=1$, $y=0$ to ...
2
votes
1answer
35 views

Getting four points on a closed non-intersecting curve such that they form a square.

Prove that in any closed non-intersecting curve there exist four points on the curve such that they make a square. I have no idea from where to start.
1
vote
0answers
47 views

Regular pentagon vector proof

Given that $v = DC = \lambda EB$, prove that $\lambda v = CB + ED$. Whatever I try seems to end up with $CB + ED = (\frac {1}{\lambda} - 1)v$, ie: $$CB + ED = CD + DE + EB + ED = EB - DC = EB - ...
2
votes
2answers
64 views

Law of Sines and Cosines

My teacher gave me the formula for law of sines, and I know how to solve questions like this, but I don't see how the theorem below can actually work. Can someone please explain?
1
vote
5answers
42 views

Central Angles of a Circle

My teacher said that the central angles of a circle are equal to the measure of the arc, but I don't understand on how this could possibly work. Can someone please explain how this is possible?
10
votes
2answers
661 views

Covering one square by three smaller squares

Consider square of side $1.25$ can it be covered by three squares of side $1$ ? I think it's impossible but I'm not sure how to show it.
1
vote
2answers
53 views

How is the Pythagorean Theorem related to the Equation of a Circle

My teacher wants me to figure out how the Pythagorean Theorem and the Equation of a Circle are related. I can't figure this out because I view them as being two completely different things. I ...
0
votes
1answer
21 views

A Vector Question on a Cube (3D Problem)

As shown in the following figure, $E$ is the mid point of $AD$; $F$ is the mid point of $AB$. Let $\theta$ be the angle formed by straight line $BC_1$ and plane $EFB_1 D_1$. Find $cos\theta$. I ...
1
vote
1answer
46 views

how to find the angles given below.

what are the steps you need to find supplementary, complementary , opposite ,corresponding and alternate angle and also scalene triangle? I seriously need help with these angles and i have asked my ...
14
votes
3answers
894 views

Prove that when dividing a square field among three people, one person must own two points more than 1 km apart

We have a square field with a $1$ km side we need to divide among three people (it doesn't have to be fair, one of them could even get none of it!). How would I prove that at least one of the persons ...