The coordinates of three vertices of square ABCD are A(−2 1/2,1 1/2),B(−2 1/2,−3),A(-2 1/2,1 1/2),B(-2 1/2,-3), and C(2,1 1/2)C(2,1 1/2).When point D is placed on this square, what will the perimeter of the square be?Enter your answer in the box.
why repeat everything? So annoying
AB = 4 1/2
so the perimeter is 4 * 4 1/2 = 18
it is called study and do your practice work!!!
it is. but its also a bit complicated and stuff were most likely not gonna use in the future
To find the perimeter of the square, we need to calculate the distance between its vertices.
Let's start by finding the distance between points A and B. We can use the distance formula:
Distance between two points (x₁, y₁) and (x₂, y₂) = √((x₂ - x₁)² + (y₂ - y₁)²)
Substituting the coordinates of points A and B:
Distance between A and B = √((-2 1/2 - (-2 1/2))² + (-3 - 1 1/2)²)
= √(0² + (-4 1/2)²)
= √(0 + (4 1/2)²)
= √(0 + 20 1/4)
= √(20 1/4)
= √(81/4)
= (√81)/2
= 9/2
So, the distance between points A and B is 9/2.
Now, let's find the distance between points B and C:
Distance between B and C = √((-2 1/2 - 2)² + (-3 - 1 1/2)²)
= √((-4 1/2)² + (-4 1/2)²)
= √((4 1/2)² + (4 1/2)²)
= √(20 1/4 + 20 1/4)
= √(40 1/2)
= √(162/4)
= (√162)/2
So, the distance between points B and C is (√162)/2.
Since the square has equal sides, the distances between A and B, B and C are equal. Therefore, the perimeter of the square is given by:
Perimeter = 4 * Distance between points A and B
= 4 * (9/2)
= 36/2
= 18
Hence, the perimeter of the square is 18.