Question

question find the distance between the two points rounding to the nearest tenth (if necessary). (-5,3) and (-2,-3)

Explanation:

Step1: Identify the 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 the values of the points

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

Step3: Calculate the squares

$(x_2 - x_1)^2=3^2 = 9$ and $(y_2 - y_1)^2=(-6)^2=36$.

Step4: Sum the squares

$(x_2 - x_1)^2+(y_2 - y_1)^2=9 + 36=45$.

Step5: Calculate the distance

$d=\sqrt{45}\approx6.7$ (rounded to the nearest tenth).

Answer:

$6.7$