Question

find the distance between the pair of points. (-5\sqrt{7}, -1) and (-4\sqrt{7}, 2) 16 3 8 4

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $x_1=-5\sqrt{7}$, $y_1 = - 1$, $x_2=-4\sqrt{7}$, $y_2 = 2$.

Step2: Calculate $x_2 - x_1$

$x_2 - x_1=-4\sqrt{7}-(-5\sqrt{7})=-4\sqrt{7}+5\sqrt{7}=\sqrt{7}$

Step3: Calculate $y_2 - y_1$

$y_2 - y_1=2-(-1)=2 + 1=3$

Step4: Substitute into distance formula

$d=\sqrt{(\sqrt{7})^2+3^2}=\sqrt{7 + 9}=\sqrt{16}=4$

Answer:

D. 4