The image shows a graph with several vectors labeled S1, S2, S3, S4, and S5. The prompt asks to calculate S1x, S1y, and |S| and to do so for each vector.

Analysis of Vectors:

• Vector S1: Starts at approximately (1, 3) and ends at approximately (2, 1).
  • Horizontal component (S1x): Approximately $$2 - 1 = 1$$
  • Vertical component (S1y): Approximately $$1 - 3 = -2$$
  • Magnitude (|S1|): Approximately $$\sqrt{(1)^2 + (-2)^2} = \sqrt{1 + 4} = \sqrt{5} \approx 2.24$$
• Vector S2: Starts at approximately (3, 5) and ends at approximately (4.5, 3).
  • Horizontal component (S2x): Approximately $$4.5 - 3 = 1.5$$
  • Vertical component (S2y): Approximately $$3 - 5 = -2$$
  • Magnitude (|S2|): Approximately $$\sqrt{(1.5)^2 + (-2)^2} = \sqrt{2.25 + 4} = \sqrt{6.25} = 2.5$$
• Vector S3: Starts at approximately (3, 2) and ends at approximately (5, 2).
  • Horizontal component (S3x): Approximately $$5 - 3 = 2$$
  • Vertical component (S3y): Approximately $$2 - 2 = 0$$
  • Magnitude (|S3|): Approximately $$\sqrt{(2)^2 + (0)^2} = \sqrt{4} = 2$$
• Vector S4: Starts at approximately (6, 2.5) and ends at approximately (6, 4).
  • Horizontal component (S4x): Approximately $$6 - 6 = 0$$
  • Vertical component (S4y): Approximately $$4 - 2.5 = 1.5$$
  • Magnitude (|S4|): Approximately $$\sqrt{(0)^2 + (1.5)^2} = \sqrt{2.25} = 1.5$$
• Vector S5: Starts at approximately (5.5, 4) and ends at approximately (6.5, 6).
  • Horizontal component (S5x): Approximately $$6.5 - 5.5 = 1$$
  • Vertical component (S5y): Approximately $$6 - 4 = 2$$
  • Magnitude (|S5|): Approximately $$\sqrt{(1)^2 + (2)^2} = \sqrt{1 + 4} = \sqrt{5} \approx 2.24$$

Note: The coordinates are approximate as they are read from the grid. The prompt requested calculations for S1x, S1y, and |S| and to repeat for each vector.