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

Kite

Step-by-step explanation:

We are given that a quadrilateral ABCD with vertices A(3,1),B(4,5),C(7,5) and D(7,2).

We have to find the type of quadrilateral.

Construction: Join A to C and B to D.

Mid- point formula

Using this formula

Mid point of diagonal AC,=(5,3)

Mid- point of diagonal of BD=

We know that diagonals of parallelogram , square and rhombus are bisect to each other.

Therefore, mid-points of both diagonal are same .

Slope formula =

When two lines are perpendicular then product of their slopes=-1

Slope of AC=

Slope of BD=

Product of slope of AC and  slope of BD=-1

Hence, diagonal AC and diagonal BD are perpendicular to each other.

But there are mid - point of both diagonal are not same.

When the perpendicular cut to each other and do not bisect to each other then the quadrilateral ABCD is kite.

Hence, the given quadrilateral is kite.

Kite