Math Snap

STEP 1

1. The dilation is centered at the origin $(0, 0)$.
2. The scale factor for the dilation is $2$.
3. The original vertices of kite QRST are given as $Q(-1, -5)$, $R(1, 2)$, $S(0, 4)$, and $T(-2, 2)$.

STEP 2

1. Understand the concept of dilation.
2. Apply the dilation transformation to each vertex.
3. Plot the new vertices on the coordinate grid.

STEP 3

Understand the concept of dilation:
A dilation with a scale factor $k$ centered at the origin transforms a point $(x, y)$ to $(kx, ky)$.

STEP 4

Apply the dilation transformation to each vertex:
- For $Q(-1, -5)$:
$$ Q' = (2 \times -1, 2 \times -5) = (-2, -10)
\] - For $R(1, 2)$:
$$ R' = (2 \times 1, 2 \times 2) = (2, 4)
\] - For $S(0, 4)$:
$$ S' = (2 \times 0, 2 \times 4) = (0, 8)
\] - For $T(-2, 2)$:
$$ T' = (2 \times -2, 2 \times 2) = (-4, 4)
\]

Plot the new vertices on the coordinate grid:
- Plot $Q'(-2, -10)$
- Plot $R'(2, 4)$
- Plot $S'(0, 8)$
- Plot $T'(-4, 4)$
Connect the vertices $Q'R'S'T'$ to form the dilated kite.
The image of kite QRST after the dilation is plotted with vertices at:
$$Q'(-2, -10), R'(2, 4), S'(0, 8), T'(-4, 4)$$