1) Select the slider tool to create a slider. [br] Name the slider [b]k[/b]. [br] Set Min = -5, Max = 5, Increment = 0.1[br][br]2) Select the DILATE FROM POINT [icon]/images/ggb/toolbar/mode_dilatefrompoint.png[/icon] tool. [br] Highlight a box around [b][color=#cc0000]point [i]A[/i][/color][/b], [color=#1e84cc][b]point [i]B[/i][/b][/color], and [b][color=#980000]Curious George's picture[/color][/b]. [br] Then select point [i]C[/i] (to serve as center of dilation)[br] In the pop-up box that appears, enter "k" (without the " " 's) to serve as the scale factor. [br][br]3) Select the Move tool. [b]Explore! [/b][br][br]Please answer the questions that appear below the applet.
Suppose point [i]P[/i] = ([i]a[/i], [i]b[/i]) is dilated about (0,0) with scale factor [i]k[/i]. [br]What would the coordinates of the image of [i]P[/i] be? [br]Express these coordinates in terms of [i]a[/i], [i]b[/i], and/or [i]k[/i].
[math]P'=\left(ka,kb\right)[/math]
Suppose point [i]P[/i] = ([i]a[/i], [i]b[/i]) is dilated about ([i]c[/i], [i]d[/i]) with scale factor [i]k[/i]. [br]What would the coordinates of the image of [i]P[/i] be? [br]Express these coordinates in terms of [i]c[/i], [i]d[/i], [i]a[/i], [i]b[/i] and/or [i]k[/i].
[math]P'=\left(c+ka,d+kb\right)[/math]
[color=#0000ff]When you're done (or if you're unsure of something), feel free to check by watching the quick silent screencast below the applet.[/color]
What do you think you were expected to learn from this exploration?
The big idea of this lesson is that dilating from the origin is different from dilating from some other point. When you dilate from the origin just multiply the coordinates of your figure by the scale factor to find the new coordinates.[br]When you dilate from some other point, like point (c,d) you multiply the scale factor time the coordinates of your figure then add c and d.