Questions and Answers
What is the y-coordinate of any point on the x-axis?
0
What are the coordinates of the origin?
(0, 0)
What is the x-coordinate of the points on the y-axis?
0
What is the y-coordinate of any point on the line through (0, 1), parallel to the x-axis?
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What is the x-coordinate of any point on the line through (1, 0), parallel to the y-axis?
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What is the length of AB in the triangle with vertices A(2,1), B(10,5)?
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Prove that triangle ABC with vertices A(2,1), B(10,5), and C(4,7) is an isosceles right triangle.
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Study Notes
Coordinate Planes
- The y-coordinate of any point on the x-axis is 0.
Coordinate Systems
- The coordinates of the origin are (0, 0).
Graphing
- The x-coordinate of points on the y-axis is 0.
Linear Graphs
- The y-coordinate of any point on the line through (0, 1), parallel to the x-axis, is 1.
Linear Graphs
- The x-coordinate of any point on the line through (1, 0), parallel to the y-axis, is 1.
Distance Formula
- The length of AB in the triangle with vertices A(2, 1), B(10, 5) can be calculated using the distance formula: √((10-2)^2 + (5-1)^2) = √(8^2 + 4^2) = √(64 + 16) = √80.
Geometry
- To prove triangle ABC with vertices A(2, 1), B(10, 5), and C(4, 7) is an isosceles right triangle:
- Calculate the lengths of the sides using the distance formula.
- Show that two sides have equal lengths.
- Verify that one of the angles is 90°.
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