Question

Calculate the distance between the points F=(-2,1) and A=(4,-2) in the coordinate plane. Round your answer to the nearest hundredth

Answer 1

Answer:

The distance between F and A is approximately 6.71 units.

Step-by-step explanation:

To find the distance between any two points, we can consider using the distance formula. Recall that:

$\displaystyle d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Let F(-2, 1) be (x₁, y₁) and A(4, -2) be (x₂, y₂).

Substitute and evaluate:

$\displaystyle \begin{aligned} FA &= \sqrt{((4) - (-2))^2 + ((-2) - (1)^2} \\ \\&=\sqrt{(6)^2 + (-3)^2} \\ \\&=\sqrt{36 + 9} \\ \\ &= \sqrt{45} \\ \\ &= 3\sqrt{5}\\ \\&\approx 6.71\text{ units} \end{aligned}$

In conclusion, the distance between F and A is approximately 6.71 units.