Question

Given the coordinates of the vertices of a quadrilateral, determine whether it is a square, a rectangle, or a parallelogram. Then find the perimeter of the quadrilateral.
A(6, –4), B(11, –4), C(11, 6), D(6, 6)
Question 5 options:

parallelogram; 50 units


rectangle; 30 units


none of these 0

square; 100 units

Answer 1

Answer:

2) ABCD is  a RECTANGLE.

Perimeter  =  30 units

Step-by-step explanation:

Here, the given points of the quadrilateral are:

A(6, –4), B(11, –4), C(11, 6), D(6, 6)

Now, if P(a,b) and Q(c,d) are any two given points, then the distance between them is given by DISTANCE FORMULA as:

$PQ = \sqrt{(c-a)^2 + (d-b)^2$

Use this to find the length of all 4 sides:

AB with coordinates A(6, –4), B(11, –4)  is given as:

$AB = \sqrt{(11-6)^2 + (-4-(-4))^2} = \sqrt{(5)^2 + 0} = 5$

⇒ AB = 5 units

BC with coordinates B(11, –4), C(11, 6)  is given as:

$BC = \sqrt{(11-11)^2 + (6-(-4))^2} = \sqrt{(0)^2 + 10^2} = 10$

⇒ BC = 10 units

CD with coordinates C(11, 6), D(6, 6)  is given as:

$CD = \sqrt{(11-6)^2 + (6-6)^2} = \sqrt{(5)^2 + 0} = 5$

⇒ CD = 5 units

AD with coordinates A(6, –4),D(6, 6)  is given as:

$AD = \sqrt{(6-6)^2 + (-4-(-4))^2} = \sqrt{(0)^2 + 10^2} = 10$

⇒ AD = 10 units

Now, here AB  = CD =  5 units, AD = BC  = 10 units

Also, in a RECTANGLE, OPPOSITE SIDES ARE EQUAL IN LENGTH.

Hence, ABCD is  a RECTANGLE.

Perimeter  = AB + BC+ CD  + AD = 5 + 10 + 5 + 10 = 30 units