Answer:
Rectangle
Step-by-step explanation:
Kite is a quadrilateral in which exactly two pair of adjacent sides are equal.
Rectangle is a quadrilateral in which opposite sides are equal.
Square and rhombus are a quadrilaterals in which all sides are equal.
Given points: \((-5,2), (-3,4), (1,0), (-1,-2)\)
We need to find whether these points represent coordinates of kite , rectangle , rhombus or square .
Let the points be \(A(-5,2), B(-3,4), C(1,0), D(-1,-2)\)
We know that distance between points \(\left (x_1,y_1 \right )\,,\,\left ( x_2,y_2 \right )\) is given by \(\sqrt{\left ( x_2-x_1 \right )^2+\left ( y_2-y_1 \right )^2}\)
\(AB=\sqrt{\left (-3+5 \right )^2+\left (4-2 \right )^2}=\sqrt{4+4}=\sqrt{8}\\BC=\sqrt{\left ( 1+3 \right )^2+\left ( 0-4 \right )^2}=\sqrt{16+16}=\sqrt{32}\\CD=\sqrt{\left ( -1-1 \right )^2+\left ( -2-0 \right )^2}=\sqrt{4+4}=\sqrt{8}\\AD=\sqrt{\left ( -1+5 \right )^2+\left ( -2-2 \right )^2}=\sqrt{16+16}=\sqrt{32}\)
Here, AB = CD and AD = BC, so the given points are coordinates of the rectangle .
