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Geometry - 2.1 & 2.2 Review
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Terms in this set (21)
What is the rule when you reflect any two points over the
x-axis
?
(x, y) turns into (x, -y)
What is the rule when you reflect any two points over the
y-axis
?
(x, y) turns into (-x, y)
What is the rule when you reflect any two points over
y = x
?
(x, y) turns into (y, x)
What is the rule when you reflect any two points over the
origin (0, 0)
?
(x, y) turns into (-x, -y)
Define a transformation.
a change in the position, shape, or size of a figure
Define a rigid motion.
a type of transformation that preserves angles and lengths of sides
- also known as a rigid transformation or isometry
Define an image.
the result of transforming a figure
Define a pre-image.
the original point/shape
What do you call the new points of a figure after it is transformed?
(original point name)'
- pronounced as prime
- ex: the image of A = A'
What are the coordinates of an image of the point (-3, 6) under a reflection in y = x?
(6, -3)
If the function g is in a reflection in the line
y = -x
, then the rule for g is...
(x, y) turns into (-y, -x)
Under a reflection in y = -x, what coordinates remain fixed under the reflection?
(0, 0)
Solve for x, y, and z.
AB = 2x + 2
BC = 20
AC = 15
A'B' = 8
B'C' = 5z
A'C' = 3y - 3
x = 3
y = 6
z = 4
Give the coordinates of the point (-5, 3) if you reflect it over the x-axis, y-axis, and y = x.
x-axis: (-5, -3)
y-axis: (5, 3)
y = x: (3, -5)
When reflecting points over a line, the points would have to be the _____________________ from the line of reflection.
When reflecting points over a line, the points would have to be the
same distance
from the line of reflection.
When connecting a point and its prime with a line segment, what angle does it make with the line of reflection? What is the relationship between these two lines?
makes a right angle — the line of reflection is a perpendicular bisector of all of the line segments between a original point and its prime
During a reflection, line segment RR' = 18 units. What is the distance from point R to the line of reflection?
9 units (18/2 = 9)
How do you construct the line of reflection of an image and a pre-image off the coordinate plane?
1. Connect any point to its image point with a line segment.
2. Using your compass, measure a distance that is larger than the distance from one end of the line segment to the midpoint.
3. Make two BIG arcs: one from the original point and one from the image point. Do not change the distance on your compass!
4. The two points where the arcs intersect are the foundations of your line of reflection. Connect them.
Given triangle ABC with vertices A(3, 5), B(-3, 0), and C(7, -4) is reflected in the x-axis, which vertex remains static (fixed)?
vertex B (-3, 0)
Given triangle ABC with vertices A(3, 5), B(-3, 0), and C(7, -4) is reflected in the x-axis, what is the value of line segment CC'?
8 units
C (7, -4)
C' (7, 4)
Find the reflection of these points (that form a quadrilateral) across the x-axis:
J (-1, 3)
Y (2, 2)
R (-3, -2)
Z (0, -2)
J' (-1, -3)
Y' (2, -2)
R' (-3, 2)
Z' (0, 2)
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