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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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Step-by-step solution
5 stepsHere'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.
Draw a Cartesian plane with an x-axis and a y-axis, intersecting at the origin (0,0).
Label the axes and mark appropriate scales (e.g., 1 unit per grid line).
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
Reflect the points about the x-axis and y-axis.
To reflect a point :
- About the x-axis: The new point is .
- About the y-axis: The new point is .
Reflect each point about the x-axis.
- For A(0, 1):
- For B(1, 2):
- For C(2, 3):
- For D(-1, 2):
- For E(-3, 1):
Reflect each point about the y-axis.
- For A(0, 1):
- For B(1, 2):
- For C(2, 3):
- For D(-1, 2):
- For E(-3, 1):
The reflected points are:
- About the x-axis:
- About the y-axis:
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