Question

The following set of coordinates represents which figure?(-5,2), (-3,4), (1,0), (-1,-2)

a)kite b) rectangle c) rhombus d) square

Answer 1

It is B, rectangle. Sort of sideways.

Answer 2

Rectangle

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
`√(\left ( x_2-x_1 \right )^2+\left ( y_2-y_1 \right )^2)`

`AB=√(\left (-3+5 \right )^2+\left (4-2 \right )^2)=√(4+4)=√(8)\\BC=√(\left ( 1+3 \right )^2+\left ( 0-4 \right )^2)=√(16+16)=√(32)\\CD=√(\left ( -1-1 \right )^2+\left ( -2-0 \right )^2)=√(4+4)=√(8)\\AD=√(\left ( -1+5 \right )^2+\left ( -2-2 \right )^2)=√(16+16)=√(32)`

Here, AB = CD and AD = BC, so the given points are coordinates of the rectangle .