Question

finding the vertex from the pre-image
the rule for the dilation of quadrilateral qrst to the image qrst is $d_{o,0.5}(x, y) \to (0.5x, 0.5y)$.
what are the coordinates of q, if q(0, 2)?
(\boxed{ }, \boxed{ })
there is a coordinate grid image with quadrilateral qrst plotted, with q at (0,2), r at (-4,0), s at (0,-4), t at (4,0)

Explanation:

To determine the coordinates of \( Q' \) after the dilation \( D_{O, 0.5}(x, y) \to (0.5x, 0.5y) \), we first need to identify the coordinates of the original point \( Q \).

Step 1: Identify the coordinates of \( Q \)

From the graph, the vertex \( Q \) is at \( (-4, 0) \) (since it lies on the x - axis, 4 units to the left of the origin).

Step 2: Apply the dilation rule

The dilation rule is \( (x, y) \to (0.5x, 0.5y) \). For the point \( Q(-4, 0) \):

• The new \( x \) - coordinate is \( 0.5\times(-4)=-2 \)
• The new \( y \) - coordinate is \( 0.5\times0 = 0 \)

So, the coordinates of \( Q' \) are \( (-2, 0) \).

\boxed{(-2, 0)}

Answer:

To determine the coordinates of \( Q' \) after the dilation \( D_{O, 0.5}(x, y) \to (0.5x, 0.5y) \), we first need to identify the coordinates of the original point \( Q \).

Step 1: Identify the coordinates of \( Q \)

From the graph, the vertex \( Q \) is at \( (-4, 0) \) (since it lies on the x - axis, 4 units to the left of the origin).

Step 2: Apply the dilation rule

The dilation rule is \( (x, y) \to (0.5x, 0.5y) \). For the point \( Q(-4, 0) \):

• The new \( x \) - coordinate is \( 0.5\times(-4)=-2 \)
• The new \( y \) - coordinate is \( 0.5\times0 = 0 \)

So, the coordinates of \( Q' \) are \( (-2, 0) \).

\boxed{(-2, 0)}