Question

question
find the distance between the two points rounding to the nearest tenth (if necessary).
(6,5) and (-3,7)

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, $x_1 = 6$, $y_1 = 5$, $x_2=-3$, $y_2 = 7$.

Step2: Calculate differences

First find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=-3 - 6=-9$, $y_2 - y_1=7 - 5 = 2$.

Step3: Square the differences

$(x_2 - x_1)^2=(-9)^2 = 81$, $(y_2 - y_1)^2=2^2 = 4$.

Step4: Sum the squared - differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=81 + 4=85$.

Step5: Calculate the distance

$d=\sqrt{85}\approx9.2$.

Answer:

$9.2$