Question

calculate the distance between the points a = (-4, -1) and h = (1, 4) in the coordinate plane. round your answer to the nearest hundredth.

Explanation:

Step1: Identify distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $(x_1,y_1)=(-4,-1)$ and $(x_2,y_2)=(1,4)$.

Step2: Substitute values

$d=\sqrt{(1-(-4))^2+(4 - (-1))^2}=\sqrt{(1 + 4)^2+(4 + 1)^2}=\sqrt{5^2+5^2}$.

Step3: Calculate squares and sum

$\sqrt{25 + 25}=\sqrt{50}$.

Step4: Simplify and round

$\sqrt{50}\approx7.07$ (rounded to the nearest hundredth).

Answer:

$7.07$