Question

The vertices of a quadrilateral are A(-1,6),B(-2,4),C(2,2)and D(3,4) write a paragraph proof to determine whether quadrilateral abcd is a rectangle

Answer 1

Answer:

The given quadrilateral is a rectangle.

Step-by-step explanation:

We are given the vertices of a quadrilateral,

We can use the slopes and modulus of all sides to determine whether it is a rectangle or not. The four sides of the quadrilateral are Ab, BC, CD and AD. So finding slopes of all sides using the formula

$Slope=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

where x_1 and y_1 are the coordinates of firsst vertex and x_2 and y_2 are coordinates of second vertex.

So.

Slopes are:

Slope of AB = 2 and Length=2.23

Slope of BC = -1/2 and length = 4.47

Slope of CD = 2 and length = 2.23

Slope of AD = -1/2 and length = 4.47

As we can see that the slope of AB and CD is equal which means that they are parallel and their lengths are also same.

Similarly BC and AD have same slope which means that they are also parallel and their lengths are also equal.

More over the product of slopes of AB and CD, BC and CD, CD and AD and AD and AB is equal to -1 which indicated that these sides are parallel to each other so it can be concluded that as the opposite sides of the quadrilateral are equal and the interior angles are 90 degrees so the quadrilateral is a rectangle ..