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

The distance between F and A is approximately 6.71 units.

Explanation:

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

`\displaystyle d = √((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 &= √(((4) - (-2))^2 + ((-2) - (1)^2) \\ \\&=√((6)^2 + (-3)^2) \\ \\&=√(36 + 9) \\ \\ &= √(45) \\ \\ &= 3√(5)\\ \\&\approx 6.71\text{ units} \end{aligned}`

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