Question

what are the coordinates of \\(d\\) when the quadrilateral is reflected across the line \\(y = x\\)?

(1, 3)
(2, 4)

Explanation:

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<reasoning>

Identify the coordinates of point D

Find the coordinates of vertex \(D\) from the given coordinate grid.
Looking at the graph, point \(D\) lies at \(x = 3\) and \(y = 1\).
Thus, the coordinates of \(D\) are \((3, 1)\).

Apply the reflection rule

Using the Coordinate Transformations knowledge point, we apply the reflection rule across the line \(y = x\).
The algebraic rule for reflecting a point \((x, y)\) across the line \(y = x\) is:
\[(x, y)
ightarrow (y, x)\]

Calculate the coordinates of D'

Substitute the coordinates of \(D(3, 1)\) into the reflection rule:
\[D(3, 1)
ightarrow D'(1, 3)\]
The coordinates of \(D'\) are \((1, 3)\).
</reasoning>

<answer>
<mcq-correct>(1, 3)</mcq-correct>
<mcq-option>(2, 4)</mcq-option>
</answer>

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"name": "y = x",
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"properties": {
"name": "D'",
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Answer:

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<reasoning>

Identify the coordinates of point D

Find the coordinates of vertex \(D\) from the given coordinate grid.
Looking at the graph, point \(D\) lies at \(x = 3\) and \(y = 1\).
Thus, the coordinates of \(D\) are \((3, 1)\).

Apply the reflection rule

Using the Coordinate Transformations knowledge point, we apply the reflection rule across the line \(y = x\).
The algebraic rule for reflecting a point \((x, y)\) across the line \(y = x\) is:
\[(x, y)
ightarrow (y, x)\]

Calculate the coordinates of D'

Substitute the coordinates of \(D(3, 1)\) into the reflection rule:
\[D(3, 1)
ightarrow D'(1, 3)\]
The coordinates of \(D'\) are \((1, 3)\).
</reasoning>

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<mcq-correct>(1, 3)</mcq-correct>
<mcq-option>(2, 4)</mcq-option>
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