Question

the coordinates of the endpoints of \\(\overline{ab}\\) are \\(a(-4, 4)\\) and \\(b(2, 1)\\). which measurement is closest to the length of \\(\overline{ab}\\) in units? \
a \quad 6.2 units \
b \quad 6.7 units \
c \quad 7.1 units \
d \quad 7.5 units

Explanation:

Step1: Recall distance formula

The distance between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Step2: Identify coordinates

Let $(x_1,y_1)=(-4,4)$ and $(x_2,y_2)=(2,1)$

Step3: Calculate differences

$x_2-x_1=2-(-4)=6$, $y_2-y_1=1-4=-3$

Step4: Square and sum differences

$(6)^2+(-3)^2=36+9=45$

Step5: Compute square root

$d=\sqrt{45}\approx6.708$

Step6: Match to closest option

$\approx6.7$ units

Answer:

B. 6.7 units