Question

ch. 1.2 - segment addition postulate
find the distance between each sets of points.
l (-2, 10) and s (-4, 3)
ls = (round to the nearest hundredth, which is 2 decimal places)

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, for points $L(-2,10)$ and $S(-4,3)$, $x_1=-2,y_1 = 10,x_2=-4,y_2 = 3$.

Step2: Substitute values into formula

$d=\sqrt{(-4-(-2))^2+(3 - 10)^2}=\sqrt{(-4 + 2)^2+(3 - 10)^2}=\sqrt{(-2)^2+(-7)^2}$.

Step3: Calculate squares and sum

$\sqrt{(-2)^2+(-7)^2}=\sqrt{4 + 49}=\sqrt{53}$.

Step4: Round to nearest hundredth

$\sqrt{53}\approx7.28$.

Answer:

$7.28$