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*y*values?

Analytical & Non-Euclidean Geometry Flashcards

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Find the slope, *m*, of the line given by the equation *y* = -4*x* + 3

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Find the distance between points A and B if A = (5,-1) and B = (2,3).

The distance between points A and B is **5**.

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What is the distance between points A and B if A = (1,0) and B = (-9,-4)?

The distance between points A and B is about **10.8**.

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What is the midpoint between (3,9) and (7,-7)?

(5,1)

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What is the midpoint between (-2,3) and (8,1)?

(3,2)

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Which quadrant contains the point (4,-5)?

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Which quadrant has -*x* & +*y* values?

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Which quadrant has -*x* & -*y* values?

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Which quadrant has +*x* & -*y* values?

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Which quadrant has positive *x* and *y* values?

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21 cards in set

This flashcard set covers the different types of geometries, including hyperbolic geometry, elliptical geometry, and Euclidean geometry. Flashcards in this set will quiz you on the definitions and differences between these types of geometries. This flashcard set also covers basic topics in analytic geometry. Check your understanding of the coordinate plane, quadrants, plotting points and graphing lines, and using the distance and midpoint formulas.

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Which quadrant has positive *x* and *y* values?

Which quadrant has +*x* & -*y* values?

Which quadrant has -*x* & -*y* values?

Which quadrant has -*x* & +*y* values?

Which quadrant contains the point (4,-5)?

What is the midpoint between (-2,3) and (8,1)?

(3,2)

What is the midpoint between (3,9) and (7,-7)?

(5,1)

What is the distance between points A and B if A = (1,0) and B = (-9,-4)?

The distance between points A and B is about **10.8**.

Find the distance between points A and B if A = (5,-1) and B = (2,3).

The distance between points A and B is **5**.

Find the slope, *m*, of the line given by the equation *y* = -4*x* + 3

Find the slope, *m*, of a line that goes through (2,2) and (8,14).

Find the slope, *m*, of the line 4*x* - 2*y* = 2

*m* = 2

4*x* - 2*y* = 2 expressed in slope-intercept form is *y* = 2*x* - 1.

Therefore, the slope is 2.

Find the equation of a line passing through the point (2,5) and parallel to the line *y* = 2*x* - 8

Parallel postulate

Given a straight line and a point not on that line, there exists only one line that passes through the point and never intersects the original line, regardless of how far the lines are extended.

Euclidean geometry

The geometry of points, lines, and shapes on flat surfaces where the parallel postulate holds true.

Non-Euclidean geometry

The geometry of points, lines, and shapes on curved surfaces where the parallel postulate does not hold true.

Two common types of non-Euclidean geometry

Spherical geometry and hyperbolic geometry

This type of geometry describes saddle shapes.

Hyperbolic geometry

The sum of the interior angles of a triangle will always be equal to 180 degrees in this type of geometry.

Euclidean geometry

The sum of the interior angles of a triangle will always be greater than 180 degrees in this type of geometry.

Spherical geometry

The sum of the interior angles of a triangle will always be less than 180 degrees in this type of geometry.

Hyperbolic geometry

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14 in chapter 16 of the course:

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Geometry 101: Intro to Geometry16 chapters | 146 lessons | 13 flashcard sets

- Solving Line & Angle Problems in Geometry: Practice Problems
- Practice with Shapes in Geometry: Practice Problems
- Basics of Geometry Flashcards
- Logic & Proof in Mathematics Flashcards
- Intro to Geometric Figures Flashcards
- Triangle Properties & Construction Flashcards
- Parallel Lines & Polygons Flashcards
- Triangle Congruence, Ratios & Proportions Flashcards
- Similar Polygons Flashcards
- Quadrilaterals Overview Flashcards
- Circles Overview Flashcards
- Conic Sections Overview Flashcards
- 3D Geometry Flashcards
- Analytical & Non-Euclidean Geometry Flashcards
- Go to Studying for Geometry 101

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