Respuesta :
Answer:
|AC| =√18 and |BD| =√68. They are not equal in length.
Step-by-step explanation:
To find |AC| and |BD| of the parallelogram, we will simply use the distance formula.
Using the line distance formula;
D = √([tex]y_{2}[/tex]-[tex]y_{1}[/tex])² + ([tex]x_{2}[/tex]-[tex]x_{1}[/tex])²
A(2,1) C(5,-2)
[tex]x_{1}[/tex] =2 [tex]y_{1}[/tex]=1 [tex]x_{2}[/tex] = 5 [tex]y_{2}[/tex] =-2
|AC| = √([tex]y_{2}[/tex]-[tex]y_{1}[/tex])² + ([tex]x_{2}[/tex]-[tex]x_{1}[/tex])²
=√(-2-1)² + (5-2)²
=√(-3)² + (3)²
=√9+9
=√18
Distance |AC| =√18
B(3,6) D (1,-2)
[tex]x_{1}[/tex] =3 [tex]y_{1}[/tex]=6 [tex]x_{2}[/tex] = 1 [tex]y_{2}[/tex] =-2
|BD| = √([tex]y_{2}[/tex]-[tex]y_{1}[/tex])² + ([tex]x_{2}[/tex]-[tex]x_{1}[/tex])²
=√(-2-6)² + (1-3)²
=√(-8)² + (-2)²
=√64+4
=√68
Distance |BD| =√68
|AC| and |BD| are not equal in length
