Question

1. the length of \\(\overline{ab}\\) with \\(a(3, -2)\\) and \\(b(7, 4)\\) is:

\\(4\sqrt{13}\\) white
\\(2\sqrt{13}\\) red
52 gray

Explanation:

Step1: Recall distance formula

The distance between $A(x_1,y_1)$ and $B(x_2,y_2)$ is $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$.

Step2: Substitute coordinates

$x_1=3,y_1=-2,x_2=7,y_2=4$.
Calculate differences: $7-3=4$, $4-(-2)=6$.

Step3: Compute distance

$\sqrt{4^2+6^2}=\sqrt{16+36}=\sqrt{52}=2\sqrt{13}$.

Answer:

B. $2\sqrt{13}$ (red)