Question

find the distance between the two points rounding to the nearest tenth (if necessary). (-6,0) and (-1,4)

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: Substitute the values

Let $(x_1,y_1)=(-6,0)$ and $(x_2,y_2)=(-1,4)$. Then $x_2 - x_1=-1-(-6)=5$ and $y_2 - y_1 = 4 - 0=4$.

Step3: Calculate the square - terms

$(x_2 - x_1)^2=5^2 = 25$ and $(y_2 - y_1)^2=4^2 = 16$.

Step4: Add the square - terms

$(x_2 - x_1)^2+(y_2 - y_1)^2=25 + 16=41$.

Step5: Calculate the distance

$d=\sqrt{41}\approx6.4$

Answer:

$6.4$