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3 years ago

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?

Mathematics

1 answer:

iren2701 [21]3 years ago

7 0

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

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-------------------------------------------------------------

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----------------------------------------------------

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