What is the perimeter of rectangle WXYZ, with vertices W(-3,7), X(-5,4), Y(1,0), and Z(3,3) to the nearest unit.
PLEASE HELP.
A. 36 UNITS
B. 30 UNITS
C. 22 UNITS
D. 11 UNITS
find the lengths WX and XY. Twice their sum is the perimeter.
Use the distance formula:
WX = √((-5-(-3))^2+(4-7)^2) = √(2^2+3^2) = √13
and so on
Would it be A then?
To find the perimeter of a rectangle, we need to calculate the sum of the lengths of all four sides.
Step 1: Calculate the distance between W and X.
The distance formula is given by:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Let's substitute the coordinates:
d1 = sqrt((-5 - -3)^2 + (4 - 7)^2)
= sqrt((-5 + 3)^2 + (4 - 7)^2)
= sqrt((-2)^2 + (-3)^2)
= sqrt(4 + 9)
= sqrt(13)
Step 2: Calculate the distance between X and Y.
Using the same distance formula:
d2 = sqrt((1 - -5)^2 + (0 - 4)^2)
= sqrt((1 + 5)^2 + (0 - 4)^2)
= sqrt(6^2 + (-4)^2)
= sqrt(36 + 16)
= sqrt(52)
Step 3: Calculate the distance between Y and Z.
Again, using the distance formula:
d3 = sqrt((3 - 1)^2 + (3 - 0)^2)
= sqrt((3 - 1)^2 + 3^2)
= sqrt(2^2 + 9)
= sqrt(4 + 9)
= sqrt(13)
Step 4: Calculate the distance between Z and W.
Using the distance formula:
d4 = sqrt((-3 - 3)^2 + (7 - 3)^2)
= sqrt((-3 - 3)^2 + (7 - 3)^2)
= sqrt((-6)^2 + 4^2)
= sqrt(36 + 16)
= sqrt(52)
Step 5: Calculate the perimeter by adding all four sides together:
Perimeter = d1 + d2 + d3 + d4
= sqrt(13) + sqrt(52) + sqrt(13) + sqrt(52)
≈ 3.61 + 7.21 + 3.61 + 7.21
≈ 21.64
To the nearest unit, the perimeter of rectangle WXYZ is 22 units.
Therefore, the correct answer is C. 22 UNITS.
To find the perimeter of a rectangle, you need to add up the lengths of all its sides.
First, let's find the lengths of the sides.
The length of side WY can be found using the formula for the distance between two points:
WY = √[(x2 - x1)² + (y2 - y1)²]
So for WY, we have:
W(-3, 7) and Y(1, 0)
WY = √[(1 - (-3))² + (0 - 7)²]
= √[(4)² + (-7)²]
= √[16 + 49]
= √[65]
≈ 8.06
The length of side XY can also be found using the distance formula:
XY = √[(x2 - x1)² + (y2 - y1)²]
So for XY, we have:
X(-5, 4) and Y(1, 0)
XY = √[(1 - (-5))² + (0 - 4)²]
= √[(6)² + (-4)²]
= √[36 + 16]
= √[52]
≈ 7.21
Given that rectangle WXYZ has four sides of equal length, we only need to find the lengths of two opposite sides and multiply them by 2 to get the perimeter.
Using the lengths we found, the perimeter of rectangle WXYZ is approximately:
Perimeter = 2 * (WY + XY)
= 2 * (8.06 + 7.21)
= 2 * 15.27
≈ 30.54
Rounding to the nearest unit, the perimeter is approximately 31 units.
Therefore, none of the provided answer choices (A, B, C, D) accurately represents the perimeter of rectangle WXYZ.