5-1: Transformations. English Casbarro Unit 5. Isometries. An isometry is a transformation that preserves both size and shape Also called a congruence transformation Reflections, translations and rotations are isometries Dilations are NOT isometries.
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(a, b) (–a, b)
(a, b) (a, –b)
(a, b) (b, a)
The line of symmetry is the line where a fold would match up both sides exactly.
Ex. A figure with vertices (2,3), (–1, 4), and (0, 2) is reflected across the x axis, State the points of the new figure.
Answer: (2, –3), (–1, –4), and (0, –2)
(a, b) (a + x, b + y)
Ex. A figure with vertices (2,3), (–1, 4), and (0, 2) is translated 4 units to the right and 3 units down.
Answer: You will add 4 to all of the x values, and subtract 3 from all of the y values.
(2+4, 3-3), (–1+4, 4-3), and (0+4, 2-3) (6, 4), (3, 1), and (4, –1)
(a, b) (–b, a)
(a, b) (–a, –b)
(a, b) (b, –a)
(a, b) (a, b)
If it says clockwise rotation, change the measure into a counterclockwise rotation to use your rules.90° clockwise is the same as 270°counterclockwise, so you’d use the rules for 270°
Counterclockwise rotations are the norm
A figure PQRST has the vertices (–1, –1), (–4, 1 ), (–2, 4), (0, 4), and (2, 1).
(a, b) (ka, kb)
where k is the scale factor of the dilation.
Ex. A figure PQRST has the vertices (–1, –1), (–4, 1 ), (–2, 4), (0, 4), and (2, 1).
Where the center is at (0,0), and r is the radius of the circle.
Here the circle has the center at (0,0) with a radius of 5
Here the circle has the center at (4, –2) with a radius of 5.
Here the circle has the center at (–3 , –7) with a radius of 9.
Example: Solve x2 + y2 = 25
x – y = –7
Example: Solve y = x2 + 3x + 2
y = 2x + 3
This is what the graph looks like. You can
estimate the solution by the graph, but if
You solve the problem, you can find the