Question

use the graph at the right. find the vertices of the image of qrtw for a dilation with center (0,0) and a scale factor of \\(\frac{1}{2}\\). \\(q\\) \\(\square\\) (simplify your answer. type an ordered pair.)

Explanation:

Step1: Identify original coordinates of Q

From the graph, the original coordinates of point \( Q \) are \( (-2, 4) \) (assuming the grid and axes, we analyze the position: x - coordinate is -2, y - coordinate is 4).

Step2: Apply dilation formula

The formula for dilation with center \((0,0)\) and scale factor \( k \) is \((x', y')=(k\times x, k\times y)\). Here, \( k = \frac{1}{2} \), \( x=-2 \), \( y = 4 \).
So, \( x'=\frac{1}{2}\times(-2)=-1 \), \( y'=\frac{1}{2}\times4 = 2 \).

Answer:

\((-1, 2)\)