Subjects geometry and algebra

Enlargement And Graph

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Enlargement And Graph


1. The first problem asks to find the centre of enlargement and state the scale factor given the scale factor is -3.2. 2. The centre of enlargement is the fixed point from which all points are enlarged or reduced. Since the scale factor is negative, the image is inverted and scaled by 3.2 times from the centre. 3. Without the diagram, the exact coordinates of the centre cannot be determined here, but the scale factor is clearly given as -3.2. 4. For the second problem, sketch the graph of $$y = 2(x - 2)^3 + 1$$. 5. This is a cubic function shifted right by 2 units and up by 1 unit, and vertically stretched by a factor of 2. 6. Key points to plot include: - At $$x=2$$, $$y=2(0)^3 + 1 = 1$$ (inflection point) - At $$x=3$$, $$y=2(1)^3 + 1 = 3$$ - At $$x=1$$, $$y=2(-1)^3 + 1 = -1$$ 7. The graph passes through these points and has the characteristic cubic shape, steepening as $$x$$ moves away from 2. 8. The line $$y = 60x - 11$$ is a straight line with slope 60 and y-intercept -11, very steep and crossing the y-axis at -11. 9. The graph description matches this line segment on the grid. Final answers: - Centre of enlargement: (depends on diagram, not provided) - Scale factor: -3.2 - Graph of $$y = 2(x - 2)^3 + 1$$ is a vertically stretched cubic shifted right 2 and up 1. - The line $$y = 60x - 11$$ is a steep straight line crossing y-axis at -11.