Transformations
You're viewing free preview questions — 4 questions previewing here — subscribe to unlock 46 more, plus the Full Question Bank, Mock Papers & Worksheets.Upgrade

Transformations — Free MYP5 Mathematics (Standard) Practice Questions

1QuestionReflectionsConcept Practice
4 marks~6 minCriterion A
A graphic designer is creating a symmetrical logo using triangle ABCABC with vertices A(0,0)A(0, 0), B(2,3)B(2, 3), and C(4,1)C(4, 1). The triangle is reflected over the line x=2x = 2 to produce triangle A′B′C′A'B'C', which forms the mirror half of the logo.
a
Deduce the coordinate rule for reflecting any point (x,y)(x, y) over the line x=2x = 2. [1]
b
Determine the coordinates of A′A', B′B', and C′C'. [2]
c
The designer claims the combined shape of triangle ABCABC and triangle A′B′C′A'B'C' is perfectly symmetrical about x=2x = 2. Justify whether this claim is correct. [1]
Question diagram

Solutions

2QuestionStretch/compressionAssessment Practice
6 marks~9 minCriterion D
A graphic designer is resizing a logo for a billboard and a business card. The logo's outline is defined by vertices A(2, 1)A(2,\ 1), B(6, 1)B(6,\ 1), C(7, 4)C(7,\ 4), and D(1, 4)D(1,\ 4). The designer applies a vertical stretch by factor 2.52.5, followed by a horizontal compression by factor 0.40.4.
a
Determine the coordinates of the transformed vertices A′A', B′B', C′C', and D′D' after both transformations are applied in the given order. [2]
b
Calculate the area of the original logo and the area of the transformed logo. Show that the two areas are equal, and explain why this result occurs. [2]
c
Advise the designer whether this transformation is suitable for both media, justifying your answer with reference to the effect of non-uniform scaling on the logo's proportions and the significance of the equal-area result. [2]
Question diagram

Solutions

3QuestionReflectionsConcept Practice
2 marks~3 minCriterion B
A graphic designer uses coordinate geometry to create a reflected logo. The original logo contains the point P(3,−5)P(3, -5). The designer reflects the entire logo across the xx-axis, as shown by the pattern below.

(2, 3)→(2, −3)(2,\ 3) \rightarrow (2,\ -3)

(−1, 5)→(−1, −5)(-1,\ 5) \rightarrow (-1,\ -5)

(4, −2)→(4, 2)(4,\ -2) \rightarrow (4,\ 2)

Deduce the general rule for reflecting any point (x,y)(x, y) across the xx-axis. [1]

State the image of P(3,−5)P(3, -5) after reflection across the xx-axis. [1]

Solutions

4QuestionStretch/compressionAssessment Practice
4 marks~6 minCriterion C
A sports analyst models the vertical height (in metres) of a ball's bounce using the function f(x)=x2f(x) = x^2, where xx is time in seconds. A new surface increases all heights by a factor of 3 and reduces the launch height by 2 metres, giving a transformed function g(x)g(x).
a
Deduce the equation of g(x)g(x). [1]
b
Calculate g(4)g(4). [1]
c
The analyst claims: "At x=4x = 4 seconds, the ball reaches a height above 50 metres, so the surface is unsuitable for regulation play." Advise the analyst whether this conclusion is supported by the model. [2]

Solutions

Questions 5-50

Unlock these questions with Premium

Sign Up →

That's every free question here — 4 of 50.

+46 more questions, plus Mock Papers & Worksheets, are waiting in Premium.

Upgrade