Question

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

(1, 3)
(2, 4)

Explanation:

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 \((1, 3)\).

Answer:

• (1, 3) (Correct answer)
• (2, 4)