1. Create points [code]A=(1,2)[/code], [code]B=(3,1)[/code], [code]C=(4,-1)[/code], and [code]D=(2,0)[/code] by using the [i]Point Tool[/i] or [i]Input Bar[/i].[br]2. Showing the label of each points by using [i]Style Bar[/i].[br]3. Choose the [i]"Name and Value"[/i] option when showing the label. [br]4. Create a rhombus [code]ABCD[/code] by using [i]Polygon Tool[/i].[br]5. Create point [code]O=(0,0)[/code] and [code]T=(-4,2)[/code] by using the [i]Point Tool[/i] or [i]Input Bar[/i].[br]6. Create vector [code]OT[/code] by using [i]Vector Tool[/i].[br]7. Choose the [i]"Name and Value"[/i] option when showing the label of point [code]T[/code] by using [i]Style Bar[/i]. [br]8. Hide point [code]O[/code] so it can’t be moved accidentally by using the [i]Show/Hide Object[/i] on [i]Style Bar[/i].[br]9. Translate the rhombus [code]ABCD[/code] by vector [code]OT[/code] using the [i]Translate by Vector Tool[/i].[br]10. Explore, consider the coordinates of each point and its shadow, then complete the following table (on the Companion Answer Sheet).
Based on your activities and observations in the table above, what is the formula for getting the image coordinates of a point translated as far as a unit horizontally and b unit vertically namely [math]\binom{a}{b}[/math]?