Question

if abcd is dilated by a factor of 2, the coordinate of d would be:

\\(d = (?, )\\)

Explanation:

Identify the coordinates of point D

Find the position of point \(D\) on the coordinate plane.
Looking at the grid:

• The x-coordinate of \(D\) is \(3\).
• The y-coordinate of \(D\) is \(-2\).

Thus, \(D = (3, -2)\).

Apply the dilation transformation

Apply a dilation centered at the origin with a scale factor of \(k = 2\).
The algebraic rule for dilation centered at the origin is:

$$(x, y) ightarrow (kx, ky)$$

Calculate the coordinates of D'

Substitute the coordinates of \(D(3, -2)\) and \(k = 2\) into the rule:

$$D' = (2 \times 3, 2 \times (-2))$$

$$D' = (6, -4)$$

Answer:

If ABCD is dilated by a factor of 2, the coordinate of D' would be:
\(D' =\) (<blank>\(6\)</blank>, <blank>\(-4\)</blank>)