All Questions
Tagged with triangles coordinate-systems
110
questions
5
votes
2
answers
151
views
Prove $XX’+ZZ’=YY’$
Let the feet of angle bisectors of triangle $ABC$ are $X,Y$ and $Z$ . The circumcircle of triangle $XYZ$ cuts off three segment from lines $AB,BC $and $CA$, let it be $XX’, YY’, ZZ’$. Prove that at ...
- 1,009
1
vote
0
answers
52
views
Can a triangle $ABC$ be translated onto another triangle $PQR$ in multiple ways?
For example, if $ABC = (0,1), (2, 3), (4, 7)$ and $PQR = (-1, -1), (1, 1), (3, 5)$, then the only way $ABC$ can be superimposed onto $PQR$ is by a translation $1$ unit left and $2$ units down. This ...
- 1,950
0
votes
1
answer
62
views
With which sign should the modulus function be opened when a point lies below the line? - HW
Question: ABC is an equilateral triangle with A(0, 0) and B(a, 0) (a > 0). L, M, and N are the foot of the perpendiculars drawn from a point P to the sides AB, BC, and CA, respectively. If P lies ...
- 11
1
vote
0
answers
222
views
Prove that incentre and excenter of a triangle are harmonic conjugates.
Given the coordinates of a triangle $A(x_1,y_1)$, $B(x_2,y_2)$, $C(x_3,y_3)$, prove that the incentre and excenter of the triangle $\triangle ABC$ are harmonic conjugates with respect to the $A$ and $...
- 101
0
votes
1
answer
267
views
How to solve it using the method of coordinates?
We need to answer two questions based on the following paragraph.
At times the methods of coordinates become effective in solving problems of properties of triangles. We may choose one vertex of the ...
- 8,338
1
vote
2
answers
85
views
Find the maximum area of a triangle
The maximum area of a triangle whose sides $a,b,c$ satisfy $0\le a\le1,1\le b\le2,2\le c\le3$
We can clearly see that $1,2,3$ as sides does not make a triangle so we can't just choose the maximum ...
2
votes
1
answer
71
views
If the triangle is revolved about its any side such that the volume of solid so obtained is $128\pi$, find the radius of the circle.
A triangle with maximum area is cut from a circle. If the triangle is revolved about its any side such that the volume of solid so obtained is $128\pi$ cm$^3$, then find the radius of the circle.
My ...
- 8,338
1
vote
0
answers
184
views
Incenter and Ex-center (Harmonic conjugate)
Consider the following diagram :
I = Incenter of a triangle ABC
P = Ex-center of a triangle ABC
AD, BR, CQ are the internal angle bisectors and BP and CP are external angle bisectors.
I had ...
- 415
0
votes
1
answer
114
views
Given the coordinates of an equilateral triangle, find the coordinates of another equilateral triangle 1/2 the scale projected above.
I have an equilateral triangle with know height, length, and 3 coordinate pairs (x, y).
Given this information, I want to determine the 3 coordinate pairs for another equilateral triangle of exactly 1/...
0
votes
1
answer
660
views
Finding number of values of slope of line L
The following question is taken from JEE practice set.
In a plane rectangular coordinate system, there are three points $A(0,\frac43), B(-1,0)$ and $C(1,0)$. The distance from point P to line BC is ...
- 8,338
4
votes
1
answer
86
views
Shortest distance between orthocenter and origin
Consider the parabola $y^2=4x$. Let $V$ be the vertex, $F$ be the focus and $P$ be a point on the parabola such that $T$ is the foot of perpendicular of point $P$ on the directrix. Find a point $P$ ...
- 4,055
2
votes
2
answers
71
views
How was the area of this triangle found using the area of a right triangle?
This type of question came up in my exam a month back and its troubling me why I wasn't able to understand it. I vaguely recall my teacher explaining you could find the area using a right triangle but ...
- 336
0
votes
1
answer
108
views
Finding possible coordinates of a right triangle given one side
You are given the coordinates of two vertices a right triangle (not specified whether or not they describe the hypotenuse), and asked which of a set of possible coordinates could describe the third ...
- 133
0
votes
1
answer
530
views
Finding the $z$ coordinate for a point within a triangle in three dimensions.
Suppose I know the coordinates $(x,y,z)$ for three vertices of a triangle and the x and y coordinates of a fourth point within the triangle. How do I calculate the $z$ for that fourth point?
I've ...
- 103
0
votes
1
answer
270
views
How would you plot co-ordinates on a grid made from equilateral triangles?
The standard square grid has two axis: x and y, how would a grid made from tesselating equilateral triangles work? (An isometric grid) Triangles don't have 2 sets of parallel sides, like squares so as ...
- 33