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Given points A(0:1), B(1:2), C(2:3), D(-1:2) and E(-3:1). a. Sketch the points on a Cartesian plane. b. Reflect the points about the x-axis y-axis. Sketch the points on the Cartesian plane.

Mathematics

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Answer

b

Ax′(0,−1),Bx′(1,−2),Cx′(2,−3),Dx′(−1,−2),Ex′(−3,−1)A_x'(0, -1), B_x'(1, -2), C_x'(2, -3), D_x'(-1, -2), E_x'(-3, -1)

Ay′(0,1),By′(−1,2),Cy′(−2,3),Dy′(1,2),Ey′(3,1)A_y'(0, 1), B_y'(-1, 2), C_y'(-2, 3), D_y'(1, 2), E_y'(3, 1)

Step-by-step solution

5 steps

Here's the solution for the homework questions.

1. Given points:
A(0; 1)
B(1; 2)
C(2; 3)
D(-1; 2)
E(-3; 1)

Part a· 3 steps

Sketch the points on a Cartesian plane.

  1. Draw a Cartesian plane with an x-axis and a y-axis, intersecting at the origin (0,0).

  2. Label the axes and mark appropriate scales (e.g., 1 unit per grid line).

  3. Plot each point according to its coordinates

    • Point A: Start at the origin, move 0 units horizontally, then 1 unit up. Mark A(0, 1).
    • Point B: Start at the origin, move 1 unit right, then 2 units up. Mark B(1, 2).
    • Point C: Start at the origin, move 2 units right, then 3 units up. Mark C(2, 3).
    • Point D: Start at the origin, move 1 unit left, then 2 units up. Mark D(-1, 2).
    • Point E: Start at the origin, move 3 units left, then 1 unit up. Mark E(-3, 1).

    (Since I cannot draw, follow the steps above to sketch the points on your Cartesian plane.)

Part b

Ax′(0,−1),Bx′(1,−2),Cx′(2,−3),Dx′(−1,−2),Ex′(−3,−1)A_x'(0, -1), B_x'(1, -2), C_x'(2, -3), D_x'(-1, -2), E_x'(-3, -1)

Reflect the points about the x-axis and y-axis.

To reflect a point (x,y)(x, y):

  • About the x-axis: The new point is (x,−y)(x, -y).
  • About the y-axis: The new point is (−x,y)(-x, y).
  1. Reflect each point about the x-axis.

    • For A(0, 1): Ax′=(0,−1)A_x' = (0, -1)
    • For B(1, 2): Bx′=(1,−2)B_x' = (1, -2)
    • For C(2, 3): Cx′=(2,−3)C_x' = (2, -3)
    • For D(-1, 2): Dx′=(−1,−2)D_x' = (-1, -2)
    • For E(-3, 1): Ex′=(−3,−1)E_x' = (-3, -1)
  2. Reflect each point about the y-axis.

    • For A(0, 1): Ay′=(0,1)A_y' = (0, 1)
    • For B(1, 2): By′=(−1,2)B_y' = (-1, 2)
    • For C(2, 3): Cy′=(−2,3)C_y' = (-2, 3)
    • For D(-1, 2): Dy′=(1,2)D_y' = (1, 2)
    • For E(-3, 1): Ey′=(3,1)E_y' = (3, 1)

    The reflected points are:

    • About the x-axis: Ax′(0,−1),Bx′(1,−2),Cx′(2,−3),Dx′(−1,−2),Ex′(−3,−1)\boxed{A_x'(0, -1), B_x'(1, -2), C_x'(2, -3), D_x'(-1, -2), E_x'(-3, -1)}
    • About the y-axis: Ay′(0,1),By′(−1,2),Cy′(−2,3),Dy′(1,2),Ey′(3,1)\boxed{A_y'(0, 1), B_y'(-1, 2), C_y'(-2, 3), D_y'(1, 2), E_y'(3, 1)}
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