Question

The coordinates of the vertices of a rectangle are (−3, 4) , (7, 2) , (6, −3) , and (−4, −1) .

Answer 1

Answer

Find out the what is the perimeter of the rectangle .

To prove

As given

The coordinates of the vertices of a rectangle are (−3, 4) , (7, 2) , (6, −3) , and (−4, −1) .

As shown in the graph given below

Name the vertices A (−3, 4) , B(7, 2) , C(6, −3) , and D(−4, −1) .

Formula

$Distance\ formula = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}}$

Vertices are A (-3, 4) and B (7,2)

$AB = \sqrt{(7 - (-3))^{2} + (2 - 4)^{2}}$

$AB = \sqrt{(10)^{2} + (-2)^{2}}$

$AB = \sqrt{100 + 4}$

$AB = \sqrt{104}$

AB = 10.2 units (approx)

As this is the rectangles

Thus  AB = CD (The opposite sides of the rectangle are equal.)

CD = 10.2 units (approx)

Now  vertices are B(7, 2) and C(6, −3)

$BC = \sqrt{(6 - 7)^{2} + (-3 -2 )^{2}}$

$BC = \sqrt{(-1)^{2} + (-5 )^{2}}$

$BC = \sqrt{26}$

BC = 5.1 units(Approx)

As this is the rectangles

Thus BC = AD (The opposite sides of the rectangle are equal.)

AD = 5.1 units

Formula

Perimeter of a rectangle =  2 (length + Breadth)

As length = 10.2 units

Breadth = 5.1 units

Put in the formula

Perimeter of a rectangle =  2 × (10.2 + 5.1)

                                         = 2 × 15.3

                                          = 30.6 units.

Therefore the perimeter of a rectangle is 30.6 units .