Question

Determine and prove what shape is formed for the given coordinates for A B C D , and then find the perimeter and area as an exact value and rounded to the nearest tenth. A ( 10 , − 6 ) , B ( 6 , − 9 ) , C ( 3 , − 5 ) , D ( 7 , − 2

Answer 1

The true statements are:

• The shape formed is a square
• The perimeter and the area of the shape is 20 units, and 25 unit squares

The coordinates of the shape are given as:

• A = (10, -6)
• B =  (6, -9)
• C = (3,-5)
• D = (7,-2)

How to determine the shape?

Start by plotting the coordinates of ABCD on the coordinate plane.

Next, connect the dots on the plane

From the connected dots, we can see that the shape formed is a square

How to calculate the area and the perimeter

Start by calculating the distance between adjacent points using the distance formula

$d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}$

So, we have:

$AB = \sqrt{(10 -6)^2 + (-6 +9)^2} = 5$

$BC = \sqrt{(6 -3)^2 + (-9 +5)^2} = 5$

$CD = \sqrt{(3 -7)^2 + (-2 +5)^2} = 5$

$DA = \sqrt{(7 -10)^2 + (-2 +6)^2} = 5$

The perimeter (P) of the shape is calculated as:

$P = 4 \times AB$

$P = 4 \times 5 = 20$

The area (A) of the shape is calculated as:

$A =AB \times BC$

$A =5 \times 5 = 25$

Hence, the perimeter and the area of the shape is 20 units, and 25 unit squares

Read more about coordinates at:

brainly.com/question/17206319