Analytical Geometry

[mansoorzahraa]

 

[MarkFL]

(1) We know:

[MATH]\overline{AD}=\overline{AB}[/MATH]
[MATH]\overline{DC}=\overline{BC}[/MATH]
Or:

[MATH](3-y_D)^2+x_D^2=10[/MATH]
[MATH](3-x_D)^2+(y_C-y_D)^2=(2-y_C)^2[/MATH]
And we also know:

[MATH]\frac{2-y_D}{3-x_D}=-\frac{3}{y_C-3}[/MATH]
Or:

[MATH]y_C=\frac{3(x_D-y_D-1)}{2-y_D}[/MATH]
So, this gives us:

[MATH](3-y_D)^2+x_D^2=10[/MATH]
[MATH](3-x_D)^2+\left(\frac{3(x_D-y_D-1)}{2-y_D}-y_D\right)^2=\left(2-\frac{3(x_D-y_D-1)}{2-y_D}\right)^2[/MATH]
Can you proceed?

 

[Steven G]

I would rotate the entire figure through point A so that point C is on the y-axis. I would then find all the coordinates of the new figure and then rotate back.