Question

the coordinates of the endpoints of \\(\overline{ab}\\) are \\(a(-4, 3)\\) and \\(b(1, -3)\\). which measurement is closest to the length of \\(\overline{ab}\\) in units?\
a 4.4 units\
b 6.0 units\
c 7.4 units\
d 7.8 units

Explanation:

Step1: Recall distance formula

For points $(x_1,y_1)$ and $(x_2,y_2)$, length = $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Step2: Substitute given coordinates

Let $A(-4,3)=(x_1,y_1)$, $B(1,-3)=(x_2,y_2)$
$\text{Length of } \overline{AB} = \sqrt{(1-(-4))^2+(-3-3)^2}$

Step3: Simplify inside the square root

$\sqrt{(5)^2+(-6)^2} = \sqrt{25+36}$

Step4: Calculate final value

$\sqrt{61} \approx 7.81$, closest to 7.8 units

Answer:

D. 7.8 units