What is the most precise term for quadrilateral ABCD with vertices A(3,1) , B(4,5) , C(7,5) , D(7,2) answer choices; A. KITE B. SQUARE C. RHOMBUS D. PARALLELOGRAM
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 = \((\frac{3+7}{2} ,\frac{1+5}{2} =(5,3)\)
Mid point of BD =\((\frac{4+7}{2} ,\frac{2+5}{2} = eq 5,3)\)
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
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