Question

1. find the distance between the two points rounding to the nearest tenth (if necessary). (-1, -3) and (7, 0)

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

Let $(x_1,y_1)=(-1,-3)$ and $(x_2,y_2)=(7,0)$. Then $x_2 - x_1=7-(-1)=8$ and $y_2 - y_1=0 - (-3)=3$.

Step3: Calculate the squares

$(x_2 - x_1)^2=8^2 = 64$ and $(y_2 - y_1)^2=3^2 = 9$.

Step4: Sum the squares

$(x_2 - x_1)^2+(y_2 - y_1)^2=64 + 9=73$.

Step5: Calculate the distance

$d=\sqrt{73}\approx 8.5$.

Answer:

$8.5$