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How to plot points A(2, 5), E(2, 1), B(4, 0), and F(-2, -1) on a Cartesian coordinate plane, and determine their locations?

Mathematics

ScanSolve AI Answer

Answer

First Quadrant\text{First Quadrant}

Positive x-axis\text{Positive x-axis}

Third Quadrant\text{Third Quadrant}

Step-by-step solution

5 steps
  1. Understand the task.

    The task is to describe how to plot the given points on a Cartesian coordinate plane. For each point (x,y)(x, y), we start at the origin (0,0)(0, 0), move xx units horizontally (right if x>0x > 0, left if x<0x < 0), and then yy units vertically (up if y>0y > 0, down if y<0y < 0).

  2. Plot point $A(2, 5)$.

    To plot A(2,5)A(2, 5):

    • Start at the origin (0,0)(0, 0).
    • Move 2 units to the right along the x-axis.
    • From there, move 5 units up parallel to the y-axis. The point A(2,5)A(2, 5) is located in the First Quadrant\boxed{\text{First Quadrant}}.
  3. Plot point $E(2, 1)$.

    To plot E(2,1)E(2, 1):

    • Start at the origin (0,0)(0, 0).
    • Move 2 units to the right along the x-axis.
    • From there, move 1 unit up parallel to the y-axis. The point E(2,1)E(2, 1) is located in the First Quadrant\boxed{\text{First Quadrant}}.
  4. Plot point $B(4, 0)$.

    To plot B(4,0)B(4, 0):

    • Start at the origin (0,0)(0, 0).
    • Move 4 units to the right along the x-axis.
    • Since the y-coordinate is 0, the point lies on the x-axis. The point B(4,0)B(4, 0) is located on the Positive x-axis\boxed{\text{Positive x-axis}}.
  5. Plot point F(−2,−1)F(-2, -1).

    To plot F(−2,−1)F(-2, -1):

    • Start at the origin (0,0)(0, 0).
    • Move 2 units to the left along the x-axis.
    • From there, move 1 unit down parallel to the y-axis. The point F(−2,−1)F(-2, -1) is located in the Third Quadrant\boxed{\text{Third Quadrant}}.
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