Transformations in the Coordinate Plane

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Presentation transcript:

Transformations in the Coordinate Plane Vocabulary

Point A point is an exact location. It has no size, only position.

Line is straight (no curves), has no thickness, and extends in both directions without end (infinitely).

Perpendicular Line Lines that are at right angles (90°) to each other. Their slopes are negative reciprocals of each other

Parallel Line Two lines on a plane that never meet. They are always the same distance apart.

Line Segment In geometry, a line segment is a part of a line that is bounded by two distinct end points, and contains every point on the line between its end points.

Distance Along A Line Also known as the distance between two points

Ray A line with a start point but no end point (it goes to infinity)

Angle The amount of turn between two straight lines that have a common end point (the vertex). A shape, formed by two lines or rays diverging from a common point (the vertex).

Right Angle An angle which is equal to 90°, one quarter of a full revolution.

Acute Angle An angle less than 90° (90° is called a Right Angle)

Obtuse Angle An obtuse angle is one which is more than 90° but less than 180° In other words, it is between a right angle and a straight angle

Straight Angle An angle whose measure is 180. It is also a line.

Reflex Angle A Reflex Angle is one which is more than 180° but less than 360°

Circle A circle is a shape with all points the same distance from its center. A circle is named by its center.

One-to-One A relationship wherein each point in a set of points is mapped to exactly one other point.

Pre-image The original figure before undergoing a transformation.

Image The new, resulting figure after a transformation

Isometry A transformation in which the preimage and image are congruent.

Every segment is congruent to its image. Transformations are called RIGID if every image is congruent to its preimage. Rigid transformations can also be referred to as an ISOMETRY. Every segment is congruent to its image.

Which of the following are rigid transformations? (Isometry)

Isometries not only preserve lengths, but they preserve angle measures parallel lines, and betweenness of points

Find the value of each variable, given that the transformation is an isometry.

Congruent Figures are congruent if they have the same shape, size, lines, and angles.

Similar Triangles Triangles are similar if they have the same shape but have different sizes.