Question

The coordinates of the endpoints of WZ are W(6, 4) and Z(2, 5).

Which measurement is closest to the length of WZ in units?
Responses
A 44
B 11
C 5.35.3
D 4.1

Answer 1

To find the length of the segment WZ with endpoints W(6, 4) and Z(2, 5), we can use the distance formula:

\[
\text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

Here, \((x_1, y_1) = (6, 4)\) and \((x_2, y_2) = (2, 5)\).

Plugging in the values, we have:

\[
\text{Distance} = \sqrt{(2 - 6)^2 + (5 - 4)^2}
\]

Calculating each component:

\[
2 - 6 = -4 \quad \Rightarrow \quad (-4)^2 = 16
\]

\[
5 - 4 = 1 \quad \Rightarrow \quad (1)^2 = 1
\]

Now, combine the results:

\[
\text{Distance} = \sqrt{16 + 1} = \sqrt{17}
\]

Calculating the square root of 17 gives approximately:

\[
\sqrt{17} \approx 4.123
\]

Given the options provided, the closest measurement to the length of WZ in units is:

D. 4.1