Question

find the distance between the two points rounding to the nearest tenth (if necessary). (3, -4) and (9, -9)

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, $x_1 = 3$, $y_1=-4$, $x_2 = 9$, and $y_2=-9$.

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$.
$x_2 - x_1=9 - 3=6$
$y_2 - y_1=-9-(-4)=-9 + 4=-5$

Step3: Square the differences

$(x_2 - x_1)^2=6^2 = 36$
$(y_2 - y_1)^2=(-5)^2 = 25$

Step4: Sum the squared - differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=36 + 25=61$

Step5: Calculate the distance

$d=\sqrt{61}\approx 7.8$

Answer:

$7.8$