Question

write the coordinates of the vertices after a dilation with a scale factor of 2, centered at the origin.
q(□, □)
r(□, □)
s(□, □)

Explanation:

Step1: Find original coordinates

From the graph, \( Q(-3, -4) \), \( R(-1, -4) \), \( S(0, 5) \) (assuming the y - coordinate of S is 5, maybe a typo in the graph label, but based on the grid, S is at (0,5)).

Step2: Apply dilation rule

Dilation centered at origin with scale factor \( k \) transforms \( (x,y) \to (kx,ky) \). For \( k = 2 \):

• For \( Q(-3,-4) \): \( Q'=(2\times(-3),2\times(-4))=(-6,-8) \)
• For \( R(-1,-4) \): \( R'=(2\times(-1),2\times(-4))=(-2,-8) \)
• For \( S(0,5) \): \( S'=(2\times0,2\times5)=(0,10) \) (Wait, maybe the original S is (0,5)? Wait, looking at the graph, S is at (0,5)? Wait, the graph has S at (0,5)? Wait, the user's graph: S is at (0,5)? Wait, the y - axis: the point S is at (0,5)? Wait, maybe I misread. Wait, the grid: the y - axis, the point S is at (0,5)? Wait, no, the original S: looking at the graph, the purple point S is at (0,5)? Wait, no, the vertical line: from the grid, the point S is at (0,5)? Wait, maybe the original coordinates: Let's re - check. The point Q: x = - 3, y=-4 (since it's 3 units left of origin on x, 4 units down on y). R: x=-1, y = - 4. S: x = 0, y = 5 (since it's on y - axis, 5 units up). Then dilation with scale factor 2: multiply each coordinate by 2.

Answer:

\( Q'(-6, -8) \), \( R'(-2, -8) \), \( S'(0, 10) \)