Respuesta :
Answer:
Step-by-step explanation:
Given are the vertices of a quadrilateral.
WE have to find the name of the quadrilateral
WE have slope of AC = (5-1)/(7-3) = 1
and slope of BD = (2-5)/(7-4) = -1
Since m1m2 =-1 we get
the diagonals cut at right angles
This property is special property for square, rhombus and kite only.
Let us check if diagonals bisect each other
Mid point of AC = [tex](\frac{3+7}{2} ,\frac{1+5}{2} =(5,3)[/tex]
Mid point of BD =[tex](\frac{4+7}{2} ,\frac{2+5}{2} =\neq 5,3)[/tex]
Since diagonals do not bisect this is neither rhombus nor square.
Only possibility is kite
The most precise term for the quadrilateral ABCD with the given vertices is; A: KITE
PROPERTIES OF QUADRILATERALS
Let us first check for the slope of the diagonals. If they intersect at right angles, then they could be square, rhombus or kite.
Slope of diagonal AC = (5 - 1)/(7 - 3) = 1
Slope of diagonal BD = (2 - 5)/(7 - 4) = -1
Thus, slope 1/slope 2 = 1/-1 = - 1
This means they intersect at a perpendicular point.
Let us know find the coordinates of their midpoints. If they are the same, then it could be a square or a rhombus. If they are different, then it is a kite.
Midpoint of AC = (7 + 3)/2 AND (5 + 1)/2 = (5, 3)
Midpoint of BD = (7 + 4)/2 AND (2 + 5)/2 = (5.5, 3.5)
They are not the same and as such this is a kite.
Read more on properties of quadrilaterals at; https://brainly.com/question/2834250
