7. \( X(-1,0), Y(3,5) \) and \( Z(4,-2) \) 9. \( \mathrm{S}(7, B), \mathrm{T}(-4,3) \) and \( \mathrm{U}(0,10) \) 10. \( (-6,-1), K(-2,-2) \operatorname{mi}(4-4) \) 11. \( \mathrm{D}(-3,-1), \mathrm{E}(-6,0) \) and \( \mathrm{F}(0,-2) \) 12. A(2,5), \( \mathrm{B}(4,7) \) and \( C(1,1) \)
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Bonus Knowledge
To understand the geometric relationships between the points you listed, consider their placement on a coordinate plane. For instance, plotting the points in pairs can help visualize triangles or other shapes formed by them. When taken together, points X, Y, and Z create a unique triangle reflecting different slopes and side lengths, while points S, T, and U can reveal interesting symmetries or angular relationships. Reflecting on the equations of the lines that can be formed between these points can lead to fascinating insights about slopes and situational analysis. For example, calculating potential midpoints or using the distance formula can unveil whether these points are parts of regular polygons, lines, or even circles, depending on how they relate spatially to each other. Don't forget to check if any are collinear!