Given information: A(13,30,9) C(2,5,17) B(bx,by,13) D(dx,dy,13), hence the height of points B and D are the same .
Need to determine bx,by,dx,dy.
Segment AC and BD are the diagonals.
Thanks
Given information: A(13,30,9) C(2,5,17) B(bx,by,13) D(dx,dy,13), hence the height of points B and D are the same .
Need to determine bx,by,dx,dy.
Segment AC and BD are the diagonals.
Thanks
Hello, Ants!
I have a game plan . . .
$\displaystyle A(13,30,9),\;B(x_b,y_b,13),\lC(2,5,17),\;D(x_d,y_d ,13)\,\text{ form a square.}$
$\displaystyle \text{Segments }AC\text{ and }BD\text{ are the diagonals.}$
$\displaystyle \text{Determine }x_b,y_b,x_d,y_d.$We have four unknowns; we will need four equations.Code:(2,5,17) ♥ C * * D * * (x_{d},y_{d},13) ♥ * * * * * * ♥ (x_{b},y_{b},13) * * B * * A ♥ (13,30,9)
The sides of the square are equal.
. . $\displaystyle \begin{array}{ccccc} \overline{AB}^2 &=& (x_b-13)^2 + (y_b-30)^2 + (13-9)^2 \\ \overline{BC}^2 &=& (x_b-2)^2 + (y_b-5)^2 + (13-17)^2 \\ \overline{CD}^2 &=& (x_d-2)^2 + (y_d-5)^2+(13-17)^2 \\ \overline{DA}^2 &=& (x_d-13)^2 + (y_d-30)^2 + (13-9)^2 \end{array}$
These give us three equations.
The diagonals are equal.
. . $\displaystyle \overline{AC}^2 \:=\:11^2 + 25^2 + 8^2 \:=\:810 \quad\Rightarrow\quad AC \:=\:9\sqrt{10}$
. . $\displaystyle \overline{BD}^2 \:=\:(x_d-x_b)^2 + (y_d-y_b)^2 + (13-13)^2$
This gives us the fourth equation.
Can you take it from here?