Question

(04.01r lc)

segment ab has point a located at (4, 2). if the distance from a to b is 3 units, which of the following could be used to calculate the coordinates for point b?

\\(3 = \sqrt{(x-2)^2 + (y-4)^2}\\)

\\(3 = \sqrt{(x-4)^2 + (y-2)^2}\\)

\\(3 = \sqrt{(x+2)^2 + (y+4)^2}\\)

\\(3 = \sqrt{(x+4)^2 + (y+2)^2}\\)

Explanation:

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<reasoning>

State the distance formula and given values

\[

$$\begin{aligned} &d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\\ &A(x_1, y_1) = (4, 2)\\ &B(x_2, y_2) = (x, y)\\ &d = 3 \end{aligned}$$

\]

Substitute the coordinates into the formula

\[
3 = \sqrt{(x - 4)^2 + (y - 2)^2}
\]
</reasoning>

<answer>
<mcq-option>(A) \(3 = \sqrt{(x-2)^2 + (y-4)^2}\)</mcq-option>
<mcq-correct>(B) \(3 = \sqrt{(x-4)^2 + (y-2)^2}\)</mcq-correct>
<mcq-option>(C) \(3 = \sqrt{(x+2)^2 + (y+4)^2}\)</mcq-option>
<mcq-option>(D) \(3 = \sqrt{(x+4)^2 + (y+2)^2}\)</mcq-option>
</answer>

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Answer:

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<reasoning>

State the distance formula and given values

\[

$$\begin{aligned} &d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\\ &A(x_1, y_1) = (4, 2)\\ &B(x_2, y_2) = (x, y)\\ &d = 3 \end{aligned}$$

\]

Substitute the coordinates into the formula

\[
3 = \sqrt{(x - 4)^2 + (y - 2)^2}
\]
</reasoning>

<answer>
<mcq-option>(A) \(3 = \sqrt{(x-2)^2 + (y-4)^2}\)</mcq-option>
<mcq-correct>(B) \(3 = \sqrt{(x-4)^2 + (y-2)^2}\)</mcq-correct>
<mcq-option>(C) \(3 = \sqrt{(x+2)^2 + (y+4)^2}\)</mcq-option>
<mcq-option>(D) \(3 = \sqrt{(x+4)^2 + (y+2)^2}\)</mcq-option>
</answer>

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