A quadrilateral has vertices
P(3,5),Q(-4,3),R(-3,-2),and S(5,-4).
Find the lengths of the diagonals,to the nearest tenth?
Maybe re-wording this question will help you out. Find the distance between two points:
a)(-4,3) and (5,-4)
b)(-3,-2) and (3,5)
I'm sure your teacher gave you this formula:
d = sqroot [(x2 - x1)^2 + (y2 - y1)^2]
where x and y are defined as (x,y) in the coordinate. x2 just mean the x in the second coordinate.
Why did the quadrilateral go to the doctor?
Because it wanted to check its diagonals!
To find the lengths of the diagonals, we can use the distance formula. Let's calculate!
For diagonal PS:
Distance = √((x₂ - x₁)² + (y₂ - y₁)²)
Distance PS = √((5 - 3)² + (-4 - 5)²)
Distance PS = √((-2)² + (-9)²)
Distance PS = √(4 + 81)
Distance PS ≈ √85 ≈ 9.2 (to the nearest tenth)
For diagonal QR:
Distance QR = √((-4 - (-3))² + (3 - (-2))²)
Distance QR = √((-1)² + (5)²)
Distance QR = √(1 + 25)
Distance QR ≈ √26 ≈ 5.1 (to the nearest tenth)
So, the length of diagonal PS is approximately 9.2, and the length of diagonal QR is approximately 5.1.
To find the lengths of the diagonals of the quadrilateral PQRS, you can use the distance formula. The distance formula is given by:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Let's calculate the lengths of the diagonals step-by-step:
1. Diagonal PQ:
P = (3, 5)
Q = (-4, 3)
Using the distance formula:
d(PQ) = √((-4 - 3)^2 + (3 - 5)^2)
= √((-7)^2 + (-2)^2)
= √(49 + 4)
= √53
≈ 7.3 (rounded to the nearest tenth)
2. Diagonal PR:
P = (3, 5)
R = (-3, -2)
Using the distance formula:
d(PR) = √((-3 - 3)^2 + (-2 - 5)^2)
= √((-6)^2 + (-7)^2)
= √(36 + 49)
= √85
≈ 9.2 (rounded to the nearest tenth)
3. Diagonal PS:
P = (3, 5)
S = (5, -4)
Using the distance formula:
d(PS) = √((5 - 3)^2 + (-4 - 5)^2)
= √((2)^2 + (-9)^2)
= √(4 + 81)
= √85
≈ 9.2 (rounded to the nearest tenth)
4. Diagonal QR:
Q = (-4, 3)
R = (-3, -2)
Using the distance formula:
d(QR) = √((-3 - (-4))^2 + (-2 - 3)^2)
= √((1)^2 + (-5)^2)
= √(1 + 25)
= √26
≈ 5.1 (rounded to the nearest tenth)
Note: The order in which you connect the vertices of the quadrilateral does not affect the length of the diagonals.
To find the lengths of the diagonals of a quadrilateral, you can use the distance formula. The distance formula is given by:
d = √((x2 - x1)² + (y2 - y1)²)
Let's find the lengths of the two diagonals PQ and RS using the given vertices.
Length of diagonal PQ:
P(3, 5) and Q(-4, 3)
Using the distance formula:
d(PQ) = √((-4 - 3)² + (3 - 5)²)
= √((-7)² + (-2)²)
= √(49 + 4)
= √53
≈ 7.3 (rounded to the nearest tenth)
So, the length of diagonal PQ is approximately 7.3 units.
Length of diagonal RS:
R(-3, -2) and S(5, -4)
Using the distance formula:
d(RS) = √((5 - (-3))² + (-4 - (-2))²)
= √(8² + (-2)²)
= √(64 + 4)
= √68
≈ 8.2 (rounded to the nearest tenth)
So, the length of diagonal RS is approximately 8.2 units.