Unit notes and practice questions
Everything here is for unit 7 of the Grade 11 Mathematics textbook: what the chapter covers, the short notes, practice questions with their answers, and the lesson video where one exists.
10 multiple-choice questions written against this chapter, each with its answer and the reason. Try one before you open the answer.
Question 1
What is the image of a point (x, y) after an anticlockwise rotation of 90° about the origin?
Answer: A (-y, x)
Why
Under a counter-clockwise rotation of 90° (θ = π/2) about the origin, any point (x, y) becomes (-y, x).
Question 2
In the study of transformations, what is a rigid motion?
Answer: B A motion that preserves distance
Why
A rigid motion is defined as a transformation of the plane that preserves distance between points.
Question 3
Given the translation (x, y) → (x + 6, y - 2), what is the image of the point (2, 6)?
Answer: C (8, 4)
Why
Substitute x = 2 and y = 6 into the rule: x' = 2 + 6 = 8 and y' = 6 - 2 = 4, giving (8, 4).
Question 4
When the angle of rotation about the origin is θ = 2πn for an integer n, what type of transformation is R?
Answer: B The identity transformation
Why
Rotating by full multiples of 2π (360°) returns every point to itself, making it the identity transformation.
Question 5
What is the image of a point (x, y) under a reflection in the line y = -x?
Answer: D (-y, -x)
Why
According to the reflection formulas in the textbook, reflection in the line y = -x maps (x, y) to (-y, -x).
Question 6
What is the image of the point A(3, 4) when it is rotated through θ = π (180°) about the point (6, 5)?
Answer: A (9, 6)
Why
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).
Question 7
What is the image of the point (x, y) under a rotation of 270° (θ = 3π/2) counter-clockwise about the origin?
Answer: B (y, -x)
Why
A counter-clockwise rotation of 270° about the origin maps (x, y) to (y, -x).
Question 8
According to the historical note in Unit 7, which statistical diagram did Florence Nightingale popularize that resembles a circular histogram?
Answer: B Rose diagram
Why
The historical note states that Florence Nightingale popularized the use of diagrams such as the rose diagram, which is like a circular histogram.
Question 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)?
Answer: B (x + 10)<sup>2</sup> + (y + 12)<sup>2</sup> = 9
Why
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.
Question 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?
Answer: A C'(-1, 2), D'(-3, 5), E'(-4, 3)
Why
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).
The app holds 21 questions on this unit, marked as you go. These are the first 10.
A lesson on this chapter from YouTube. It loads only when you press play.
Comparing distributions using summary statistics · Watch on YouTube
Unit 7 runs from page 355 to page 412 of the Ministry of Education edition.
Ministry of Education edition, English, 494 pages
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