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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 \( C(1,1) \)

Ask by Malone Gonzalez. in the United States
Mar 12,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

You've listed several sets of points in a coordinate system. To help you effectively, please specify the task you'd like to perform, such as finding distances, areas, midpoints, slopes, or checking collinearity among the points.

Solution

It seems like you have provided a list of points in a coordinate system. To assist you effectively, I need to know what specific problem or question you would like to solve with these points. Here are some common tasks that can be performed with points in a coordinate system: 1. **Finding the distance between two points.** 2. **Calculating the area of a triangle formed by three points.** 3. **Determining the midpoint of a line segment between two points.** 4. **Finding the slope of the line between two points.** 5. **Checking if three points are collinear.** Please specify what you would like to do with the points you've provided!

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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!

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