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

the circle one

answer:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,