Math Problem Statement
A square is drawn on a coordinate grid. One side lies on the line y = 3, another on y = 7, and another on x = 8. There are two lines that the final side could lie on. Work out the equation of each line.
Solution
To solve this problem:
Given:
- The square lies on a coordinate grid.
- One side lies on , another on , and another on .
The task is to determine the equations of the two possible lines that could represent the final side of the square.
Steps:
-
Visualize the square:
- A square has four sides of equal length, and its sides are either horizontal or vertical in this setup.
- Given that one horizontal side lies on and another on , these two lines represent opposite sides of the square.
- One vertical side lies on , so the square's fourth side must be another vertical line parallel to .
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Determine the position of the final side:
- Since the square is defined by equal side lengths, the distance between and is 4. Therefore, the side of the square is 4 units long.
- The fourth side must also be 4 units away from , meaning the possible locations are:
- 4 units to the left: .
- 4 units to the right: .
Final Answer:
The two possible equations for the final side of the square are:
Would you like a detailed diagram or additional explanation?
Related Questions:
- How would this solution change if the square were rotated?
- What would be the coordinates of the vertices of this square?
- Could this setup apply to rectangles, and how would the solution change?
- How do we verify the lengths of the square sides from the equations?
- What would happen if one of the sides was along a diagonal?
Tip:
Always visualize geometric problems on a coordinate grid to ensure the relationships between the lines and points are clear.
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Math Problem Analysis
Mathematical Concepts
Coordinate Geometry
Properties of Squares
Parallel Lines
Formulas
Distance between two points
Properties of squares: equal sides and parallel lines
Theorems
Definition of a square: Four equal sides and four right angles
Suitable Grade Level
Grades 7-10