የምዕራፍ ማስታወሻዎችና የመልመጃ ጥያቄዎች
በዚህ ገጽ ያለው ሁሉ ለ11ኛ ክፍል የሒሳብ መፅሐፍ ምዕራፍ 7 ነው፦ ምዕራፉ የሚሸፍነው፣ አጭር ማስታወሻዎቹ፣ የመልመጃ ጥያቄዎች ከመልሶቻቸው ጋር፣ እና ቪዲዮ ባለበት የትምህርቱ ቪዲዮ።
በዚህ ምዕራፍ ላይ የተጻፉ 10 የምርጫ ጥያቄዎች፣ እያንዳንዳቸው መልሱና ምክንያቱ አላቸው። መልሱን ከመክፈትዎ በፊት ይሞክሩ። ጥያቄዎቹ በእንግሊዝኛ ናቸው።
ጥያቄ 1
What is the image of a point (x, y) after an anticlockwise rotation of 90° about the origin?
መልስ፦ A (-y, x)
ምክንያቱ
Under a counter-clockwise rotation of 90° (θ = π/2) about the origin, any point (x, y) becomes (-y, x).
ጥያቄ 2
In the study of transformations, what is a rigid motion?
መልስ፦ B A motion that preserves distance
ምክንያቱ
A rigid motion is defined as a transformation of the plane that preserves distance between points.
ጥያቄ 3
Given the translation (x, y) → (x + 6, y - 2), what is the image of the point (2, 6)?
መልስ፦ C (8, 4)
ምክንያቱ
Substitute x = 2 and y = 6 into the rule: x' = 2 + 6 = 8 and y' = 6 - 2 = 4, giving (8, 4).
ጥያቄ 4
When the angle of rotation about the origin is θ = 2πn for an integer n, what type of transformation is R?
መልስ፦ B The identity transformation
ምክንያቱ
Rotating by full multiples of 2π (360°) returns every point to itself, making it the identity transformation.
ጥያቄ 5
What is the image of a point (x, y) under a reflection in the line y = -x?
መልስ፦ D (-y, -x)
ምክንያቱ
According to the reflection formulas in the textbook, reflection in the line y = -x maps (x, y) to (-y, -x).
ጥያቄ 6
What is the image of the point A(3, 4) when it is rotated through θ = π (180°) about the point (6, 5)?
መልስ፦ A (9, 6)
ምክንያቱ
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).
ጥያቄ 7
What is the image of the point (x, y) under a rotation of 270° (θ = 3π/2) counter-clockwise about the origin?
መልስ፦ B (y, -x)
ምክንያቱ
A counter-clockwise rotation of 270° about the origin maps (x, y) to (y, -x).
ጥያቄ 8
According to the historical note in Unit 7, which statistical diagram did Florence Nightingale popularize that resembles a circular histogram?
መልስ፦ B Rose diagram
ምክንያቱ
The historical note states that Florence Nightingale popularized the use of diagrams such as the rose diagram, which is like a circular histogram.
ጥያቄ 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)?
መልስ፦ B (x + 10)<sup>2</sup> + (y + 12)<sup>2</sup> = 9
ምክንያቱ
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.
ጥያቄ 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?
መልስ፦ A C'(-1, 2), D'(-3, 5), E'(-4, 3)
ምክንያቱ
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).
መተግበሪያው በዚህ ምዕራፍ ላይ 21 ጥያቄዎች አሉት፤ እየሠሩ ያርምዎታል። እዚህ ያሉት የመጀመሪያዎቹ 10 ናቸው።
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