Given that Segment AC is a part of Segment AB, position Point B so that the [i]part to part[/i] and [i]part to whole[/i] ratios are correct. Click on [b]Show Right Triangle[/b] for a hint if necessary, and to see the correct segment partitioning. Move the Green and Red sliders to try other partitions, and move A and C to try other segments.
1) Given that point A is (-8,6) and point C is (-4,2), what is the length of [math]\text{\overline{AC} }[/math]? (Explain how you found your solution.)
2) Given that point A is (-8,6) and point C is (-4,2), find the slope of [math]\text{\overline{AC}}[/math]. (Explain how you found your solution.)
3) Using the length of [math]\text{\overline{AC}}[/math] from question 1, and the ratios given in the file above, find the length of [math]\text{\overline{CB}}[/math], length of [math]\text{\overline{AB}}[/math], and the coordinates of point B.
4) Select the Show Right Triangle button (a triangle and some checkboxes appear), then investigate and describe how the concepts of slope, right triangles, Pythagorean theorem, and similar triangles apply to answering questions 1, 2, and 3.
5) Fill in the able :[br][table][tr][td]AC:AB [/td][td]AC:CB [/td][td] A [/td][td] C [/td][td] B [/td][/tr][tr][td]_______[/td][td] 4:5[/td][td](-8,1)[/td][td](-4,5)[/td][td]______[/td][/tr][tr][td] 3:7[/td][td]_______[/td][td](5,-4)[/td][td](2,-1)[/td][td]______[/td][/tr][tr][td]_______[/td][td]_______[/td][td](6,-6)[/td][td](-1,2)[/td][td]______[/td][/tr][/table]