Yaadannoo boqonnaa fi gaaffii shaakalaa
Wanti fuula kana irra jiru hundi boqonnaa 7 kitaaba Herrega kutaa 11 tiif: wanta boqonnaan haguugu, yaadannoo gabaabaa, gaaffii shaakalaa deebii isaanii waliin, fi viidiyoo barnootaa bakka jirutti.
Gaaffii filannoo 10 boqonnaa kana irratti barreeffaman, tokkoon tokkoon isaanii deebii fi sababa qabu. Deebii banuu dura yaali. Gaaffiin kun Ingiliffaa tiin.
Gaaffii 1
What is the image of a point (x, y) after an anticlockwise rotation of 90° about the origin?
Deebii: A (-y, x)
Sababa
Under a counter-clockwise rotation of 90° (θ = π/2) about the origin, any point (x, y) becomes (-y, x).
Gaaffii 2
In the study of transformations, what is a rigid motion?
Deebii: B A motion that preserves distance
Sababa
A rigid motion is defined as a transformation of the plane that preserves distance between points.
Gaaffii 3
Given the translation (x, y) → (x + 6, y - 2), what is the image of the point (2, 6)?
Deebii: C (8, 4)
Sababa
Substitute x = 2 and y = 6 into the rule: x' = 2 + 6 = 8 and y' = 6 - 2 = 4, giving (8, 4).
Gaaffii 4
When the angle of rotation about the origin is θ = 2πn for an integer n, what type of transformation is R?
Deebii: B The identity transformation
Sababa
Rotating by full multiples of 2π (360°) returns every point to itself, making it the identity transformation.
Gaaffii 5
What is the image of a point (x, y) under a reflection in the line y = -x?
Deebii: D (-y, -x)
Sababa
According to the reflection formulas in the textbook, reflection in the line y = -x maps (x, y) to (-y, -x).
Gaaffii 6
What is the image of the point A(3, 4) when it is rotated through θ = π (180°) about the point (6, 5)?
Deebii: A (9, 6)
Sababa
Using x' = a + (x - a)cos(π) - (y - b)sin(π) = 6 + (3 - 6)(-1) - 0 = 9 and y' = 5 + (3 - 6)sin(π) + (4 - 5)cos(π) = 5 + 0 + (-1)(-1) = 6, the image is (9, 6).
Gaaffii 7
What is the image of the point (x, y) under a rotation of 270° (θ = 3π/2) counter-clockwise about the origin?
Deebii: B (y, -x)
Sababa
A counter-clockwise rotation of 270° about the origin maps (x, y) to (y, -x).
Gaaffii 8
According to the historical note in Unit 7, which statistical diagram did Florence Nightingale popularize that resembles a circular histogram?
Deebii: B Rose diagram
Sababa
The historical note states that Florence Nightingale popularized the use of diagrams such as the rose diagram, which is like a circular histogram.
Gaaffii 9
What is the equation of the image circle when (x + 4)2 + (y - 6)2 = 9 is rotated through θ = π about the point (-7, -3)?
Deebii: B (x + 10)<sup>2</sup> + (y + 12)<sup>2</sup> = 9
Sababa
The original center is (-4, 6) with radius 3. Rotating the center 180° about (-7, -3) gives the new center (-10, -12). The radius remains 3, so the image equation is (x + 10)2 + (y + 12)2 = 9.
Gaaffii 10
A triangle has vertices C(2, 1), D(5, 3), and E(3, 4). What are the image vertices when the triangle is rotated about the origin through θ = π/2?
Deebii: A C'(-1, 2), D'(-3, 5), E'(-4, 3)
Sababa
Rotation of 90° (π/2) about the origin uses the rule (x, y) → (-y, x). Thus, C(2, 1) → (-1, 2), D(5, 3) → (-3, 5), and E(3, 4) → (-4, 3).
Appiin boqonnaa kana irratti gaaffii 21 qaba; utuu hojjettuu ni sirreessa. Kan asii jiran 10 jalqabaa ti.
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Comparing distributions using summary statistics · YouTube irratti ilaali
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