Rectangle side is represented by (2,3) and (-6,4). Find the perimeter of rectangle.
Could someone please help~
x1 = 2
x2 = -6
y1 = 3
y2 = 4
Length of first side :
a = x1 - x2
a = 2 - ( - 6 )
a = 2 + 6 = 8
Length of second side :
b = | ( y1 - y2 ) |
b = | 3 - 4 |
b = | - 1 |
b = 1
P = 2 ( a + b )
P = 2 ( 8 + 1 )
P = 2 * 9 = 18
Remark :
| |
mean absolute value
Thank you for answering.
Don't I have to find the magnitude then use square root of the answer and multiply by 2? If so, could you show it.
Sure, I can help you with that! To find the perimeter of a rectangle, we need to add up the lengths of all four sides.
First, let's find the length of one side using the distance formula:
To find the distance between two points (x1, y1) and (x2, y2), we use the following formula:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
For the first side:
Point A = (2, 3)
Point B = (-6, 4)
Using the distance formula, we can calculate the length of side AB:
Distance AB = √((-6 - 2)^2 + (4 - 3)^2)
= √((-8)^2 + (1)^2)
= √(64 + 1)
= √65
So, the length of one side of the rectangle, AB, is √65.
Next, we need to find the length of the other side. The opposite sides of a rectangle are equal in length, so we can use the same value of √65 for both sides.
Now, to find the perimeter, we add up the lengths of all four sides:
Perimeter = 2 * (length of side AB) + 2 * (length of the other side)
Perimeter = 2 * √65 + 2 * √65
= 4 * √65
Therefore, the perimeter of the rectangle is 4 times the square root of 65 or 4√65.