Question

The points A(2,1), B(3,6), C(5,-2) and D (1,-2) are the vertices of a parallelogram.fine |AC| and |BD|.are they equal in length?

Answer 1

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 = √($y_{2}$-$y_{1}$)² + ($x_{2}$-$x_{1}$)²

A(2,1)     C(5,-2)

$x_{1}$ =2    $y_{1}$=1   $x_{2}$ = 5   $y_{2}$ =-2

|AC|  = √($y_{2}$-$y_{1}$)² + ($x_{2}$-$x_{1}$)²

          =√(-2-1)² + (5-2)²

           =√(-3)² + (3)²

           =√9+9

            =√18

Distance  |AC| =√18

B(3,6)     D (1,-2)

$x_{1}$ =3    $y_{1}$=6   $x_{2}$ = 1   $y_{2}$ =-2

|BD|  = √($y_{2}$-$y_{1}$)² + ($x_{2}$-$x_{1}$)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