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2 years ago

6

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

dth

1 answer:

Anton [14]2 years ago

8 0

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 (<em>x</em>₁, <em>y</em>₁) and A(4, -2) be (<em>x</em>₂, <em>y</em>₂).

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 <em>F</em> and <em>A</em> is approximately 6.71 units.

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3 years ago

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<h2>Answer</h2>

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<h2>Explanation</h2>

Lets solve our system of equations step by step

$x^2+y^2=6$ equation (1)

$x^2-y=6$ equation (2)

1. Solve for $x^2$ in equation (2)

$x^2-y=6$

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2. Replace equation (3) in equation (1) and solve for $y$

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$6+y+y^2=6$

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3. Replace the values of $y$ in equation (3) and solve for $x$

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$x^2=6$

$x=\sqrt{6}$ or $x=-\sqrt{6}$

- For $y=-1$

$x^2=6+y$

$x^2=6-1$

$x^2=5$

$x=\sqrt{5}$ or $x=-\sqrt{5}$

So, the solutions of our system of equation are:

$x=\sqrt{6}, y=0\\ x=-\sqrt{6} , y=0\\x=\sqrt{5} , y=-1\\x=-\sqrt{5} , y=-1$

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