Questions on the use of algebraic techniques to prove geometric theorems.

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0
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7answers
879 views

Perpendicular bisector

"Show that BE is the perpendicular bisector to AC" I tried to prove this through Pythagoras, but the answer I got did not prove it was at a right angle, and therefore said it was not the ...
2
votes
5answers
1k views

Cartesian Equation for the perpendicular bisector of a line

Find the Cartesian equation for the perpendicular bisector of the line joining A(2,3) and B(0,6) How do I do this? Thank you!
8
votes
3answers
1k views

Minimal Ellipse Circumscribing A Right Triangle

Find the equation of the ellipse circumscribing a right triangle whose lengths of it's sides are $3,4,5$ and such that its area is the minimum possible one. You may chose the origin and orientation ...
4
votes
3answers
4k views

Find the coordinates in an isosceles triangle

Given: $A = (0,0)$ $B = (0,-10)$ $AB = AC$ Using the angle between $AB$ and $AC$, how are the coordinates at C calculated?
4
votes
1answer
567 views

Collective Term for $XY, YZ$ and $ZX$ Planes

Is there a collective term for the $XY, YZ$ and $ZX$ planes in $3D$ co-ordinate geometry? I was thinking "principal planes" but I'm not sure where I heard that.
4
votes
1answer
2k views

Proving the Shoelace Method at the Precalculus Level

Using only precalculus mathematics (including that the area of the triangle with vertices at the origin, $(x_1,y_1)$, and $(x_2,y_2)$ is half of the absolute value of the determinant of the $2\times ...