Quadrilateral abcd has coordinates a (3, 1), b (4, 4), c (7, 5), d (6, 2). quadrilateral abcd is a

The quadrilateral ABCD is a rhombus

Step-by-step explanation:

Given coordinates : A(3,1)  B(4,4)  C(7,5) and D(6,-2)

Firstly we will find the slope of all the four sides

{Slope = } where (x1,y1) and (x2,y2) are the coordinates of two points

Slope of AB =  

=

=3

Similarly

Slope of BC =

=

Slope of CD =

=

=3

Slope of DA

=

=

Here slope of (AB and CD) & (BC and DA) are equal

So AB ║ CD and BC║ DA         {parallel lines have equal slope}

Also product of slope  of AB and CD =1

So they are not perpendicular             {Product of ⊥ lines =-1}

Hence it  is a parallelogram

Now the length of AB = √((4-1)² +(4-3)²)

=√(3² + 1²)

=√(9+1)

=√10

Similarly BC =√10

CD =√ 10 and DA =√10

So all the sides of quadrilateral are equal

Hence it is a rhombus

y=x+9

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step-by-step explanation: