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 exac

Question

3 years ago

12

t value and rounded to the nearest tenth. A ( 10 , − 6 ) , B ( 6 , − 9 ) , C ( 3 , − 5 ) , D ( 7 , − 2

1 answer:

Paha777 [63] · Answer 1 · 2022-08-17T09:51:51+03:00

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:

<h3>How to determine the shape?</h3>

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

<h3>How to calculate the area and the perimeter</h3>

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