Question

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

Explanation:

Step1: Identify distance formula

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

Step2: Assign values

Let $(x_1,y_1)=(6,5)$ and $(x_2,y_2)=(-3,7)$. Then $x_2 - x_1=-3 - 6=-9$ and $y_2 - y_1=7 - 5 = 2$.

Step3: Calculate squares

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

Step4: Sum squares

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

Step5: Find distance

$d=\sqrt{85}\approx 9.22$.

Answer:

$\sqrt{85}\approx9.22$