Math Problem Statement

constructing the coordinate plane 1/5, 4/5, - 3/5, 2/5 -1 1/5, - 4/5, 1/5, - 2/5

Solution

To construct the coordinate plane with the given points, we need to treat each pair of numbers as coordinates (x,y)(x, y). Let's list out each pair of coordinates based on the values provided:

  1. (15,45)\left( \frac{1}{5}, \frac{4}{5} \right)
  2. (35,25)\left( -\frac{3}{5}, \frac{2}{5} \right)
  3. (1,15)(-1, \frac{1}{5})
  4. (45,15)\left( -\frac{4}{5}, \frac{1}{5} \right)
  5. (15,25)\left( \frac{1}{5}, -\frac{2}{5} \right)

Plotting Procedure:

  1. Draw the coordinate plane: Draw the x-axis (horizontal) and y-axis (vertical). Mark the points with even spacing to represent the fractional coordinates.
  2. Plot the points:
    • For (15,45)\left( \frac{1}{5}, \frac{4}{5} \right), go right 15\frac{1}{5} on the x-axis and up 45\frac{4}{5} on the y-axis.
    • For (35,25)\left( -\frac{3}{5}, \frac{2}{5} \right), move left 35\frac{3}{5} on the x-axis and up 25\frac{2}{5} on the y-axis.
    • For (1,15)(-1, \frac{1}{5}), move left 1 unit and up 15\frac{1}{5}.
    • For (45,15)\left( -\frac{4}{5}, \frac{1}{5} \right), move left 45\frac{4}{5} and up 15\frac{1}{5}.
    • For (15,25)\left( \frac{1}{5}, -\frac{2}{5} \right), move right 15\frac{1}{5} and down 25\frac{2}{5}.

Would you like me to generate an image of the coordinate plane with these points?

Related Questions:

  1. What is the distance between two points on the coordinate plane?
  2. How do you find the midpoint between two coordinates?
  3. How do you reflect a point across the x-axis or y-axis?
  4. How can you use these points to form a geometric shape?
  5. How can you calculate the slope between two points?

Tip: Always label your axes and mark the scale properly when plotting points to avoid confusion.

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Math Problem Analysis

Mathematical Concepts

Coordinate Geometry
Graphing Points
Fractions

Formulas

Coordinate plane formula: (x, y)
Distance formula: d = √((x2 - x1)^2 + (y2 - y1)^2)

Theorems

Pythagorean theorem for distance calculation
Basic properties of coordinate systems

Suitable Grade Level

Grades 6-8