1. **Problem Statement:** We have a line segment with endpoints at $A(2,4)$ and $B(4,2)$. We want to perform a dilation on this segment and find the coordinates of the endpoints after dilation. 2. **Formula for Dilation:** If a point $P(x,y)$ is dilated by a scale factor $k$ from the origin, the new point $P'(x',y')$ is given by: $$x' = kx$$ $$y' = ky$$ 3. **Important Rules:** - The center of dilation is the origin $(0,0)$ unless otherwise specified. - The scale factor $k$ stretches or shrinks the figure. - Coordinates are multiplied by $k$ to get the new coordinates. 4. **Apply Dilation:** Given $k$ (from the slider, slightly above 1, but since no exact value is given, we keep it symbolic as $k$): - Original point $A(2,4)$ becomes $A'(2k,4k)$ - Original point $B(4,2)$ becomes $B'(4k,2k)$ 5. **Endpoints:** - Original segment endpoints: $A(2,4)$ and $B(4,2)$ - Dilated segment endpoints: $A'(2k,4k)$ and $B'(4k,2k)$ This shows how the segment is transformed by dilation with scale factor $k$ from the origin. **Final answer:** - Original endpoints: $A(2,4)$, $B(4,2)$ - Dilated endpoints: $A'(2k,4k)$, $B'(4k,2k)$