Question

The points (4,3),(-4,3),(-4,-3) and (4,-3) taken in the order form the vertices of * 1 point Square Rectangle Rhombus None of these​

Answer 1

$\large\underline{\sf{Solution-}}$

Given coordinates are

Coordinates of A be (4, 3)

Coordinates of B (- 4, 3)

Coordinates of C (- 4, - 3)

Coordinates of D (4, - 3).

[ Please see the attachment ].

From graph we concluded that

AB = 8 units

BC = 6 units

CD = 8 units

DA = 6 units

Also,

AB is perpendicular to BC.

BC is perpendicular to CD

CD is perpendicular to DA

DA is perpendicular to AB.

It implies, AB = CD = 8units and BC = DA = 6 units.

As we know that,

In a quadrilateral, if all the opposite sides are equal and angle between the sides is 90°, then quadrilateral is a rectangle.

So, this figure, ABCD is a rectangle.

Additional Information :-

Let's solve the same type of problem!!!

Question The points taken in order (2, 3), (2, 1), (0, 1) and (0, 3) form vertices of

(a) Square

(b) Rhombus

(c) Rectangle

(d) None of these

Solution :-

Given coordinates are

Coordinates of A be (2, 3)

Coordinates of B (2, 1)

Coordinates of C (0, 1)

Coordinates of D (0, 3).

[ Please see the attachment ].

From graph we concluded that

AB = 2 units

BC = 2 units

CD = 2 units

DA = 2 units

Also,

AB is Perpendicular to BC.

BC is perpendicular to CD

CD is perpendicular to DA

DA is perpendicular to AB.

It implies, AB = BC = CD = DA = 2 units.

As we know that,

In a quadrilateral, if all the 4 sides are equal and angle between the sides is 90°, then quadrilateral is a square.

So, this figure, ABCD is a square.