find the distance between (2/3,4) and
(5/3,7)
a)3.16
b)4.24
c)3.46
d)10.06
a)3.16
The difference in x-coordinates (5/3-2/3)=1
The difference in y-coordinates (7-4)=3
The distance between the two points is the same as the length of the diagonal of a right triangle with legs 1 and 3, namely
L=√(1²+3²)
=√10
=3.162...
To find the distance between two points in a two-dimensional coordinate system, you can use the distance formula:
√((x2 - x1)^2 + (y2 - y1)^2)
Given the coordinates (2/3,4) and (5/3,7), we can use these values in the formula. Let's calculate the distance step by step:
Step 1: Identify the coordinates:
(x1, y1) = (2/3, 4)
(x2, y2) = (5/3, 7)
Step 2: Calculate the differences:
Δx = x2 - x1 = (5/3) - (2/3) = (3/3) = 1
Δy = y2 - y1 = 7 - 4 = 3
Step 3: Square the differences:
(Δx)^2 = (1)^2 = 1
(Δy)^2 = (3)^2 = 9
Step 4: Add the squared differences:
(Δx)^2 + (Δy)^2 = 1 + 9 = 10
Step 5: Take the square root:
√(10) ≈ 3.16
So, the distance between the points (2/3,4) and (5/3,7) is approximately 3.16. Therefore, the correct option is a) 3.16.