Coordinate Geometry and Transformations

You're viewing free preview questions — 4 questions previewing here — subscribe to unlock 199 more, plus the Full Question Bank, Mock Papers & Worksheets.Upgrade

Coordinate Geometry and Transformations — Free MYP4 Mathematics (Extended) Practice Questions

1QuestionSymmetry and reflectionAssessment Practice

6 marks~9 minCriterion D

A graphic designer is creating a logo for a café. The left half of the logo is a quadrilateral with vertices

A(1, 2)

B(2, 4)

C(3, 2)

D(2, 0)

, joined in order. The designer reflects this quadrilateral over the line

x = 5

to produce the right half, with images

A'

B'

C'

D'

.

The diagram shows the left half plotted on a coordinate grid.

State the coordinates of

A'

B'

C'

, and

D'

after reflection over the line

x = 5

. [1]

The designer makes a consistent measurement error: every reflected point is placed

0.3

units too far to the right of its correct position. Write down the erroneous coordinates of

A'

B'

C'

D'

, and calculate the percentage error in the

x

-coordinate of

B'

, giving your answer to one decimal place.

\text{percentage error} = \frac{|\text{measured} - \text{correct}|}{|\text{correct}|} \times 100\%

[3]

The designer claims the

0.3

-unit error is small enough that the completed logo still looks symmetric about

x = 5

. Assess this claim, and suggest one limitation of relying on a coordinate grid with

1

-unit spacing to detect this type of error in a real logo design. [2]

Solutions

2QuestionMovement on a plane – isometric transformations, enlargements, tessellationsAssessment Practice

6 marks~9 minCriterion B

The diagram shows the first three figures of a pattern made from unit squares arranged in an L-shape.

Figure 1 has 3 unit squares, Figure 2 has 7 unit squares, and Figure 3 has 13 unit squares.

Write down the number of unit squares in Figure 4. [1]

Find a rule for the number of unit squares

S

in Figure

n

, giving your answer in the form

S = an^2 + bn + c

, where

a

b

and

c

are integers. Show clearly how you obtained your values of

a

b

and

c

. [3]

Show that the total number of unit squares across Figure

n

and Figure

n+1

can be written as

2(n^2 + 2n + 2)

. Hence justify why this total is always even for every positive integer

n

. [2]

Solutions

3QuestionMovement on a plane – isometric transformations, enlargements, tessellationsAssessment Practice

6 marks~9 minCriterion A

The diagram shows the first four figures of a pattern. Each figure is a triangle with vertices

A^{(n)}

B^{(n)}

C^{(n)}

. Figure 1 has

A^{(1)} = (1, 1)

B^{(1)} = (3, 1)

C^{(1)} = (2, 4)

. Each new figure is obtained by translating the previous triangle 3 units in the

x

-direction and 2 units in the

y

-direction.

Write down the coordinates of

A^{(3)}

. [1]

Find a general rule for the coordinates of

A^{(n)}

, where

n

is a positive integer. [2]

A designer claims that Figure 21 is the first figure for which both coordinates of

A^{(n)}

exceed 40. Justify whether this claim is correct. [3]

Solutions

4QuestionCoordinate geometry (distance, midpoint, gradient formulas)Assessment Practice

8 marks~12 minCriterion C

The diagram shows four points

A(1,\, 2)

B(3,\, 6)

C(6,\, 12)

, and

D(4,\, 9)

plotted on a coordinate grid.

Show that

A

B

, and

C

are collinear by calculating the gradients of

AB

and

AC

, and stating what these values imply. [3]

A fifth point

P(k,\, 4k-4)

lies on the line through

A

B

, and

C

. Find the value of

k

. [2]

A student claims that because

D(4,\, 9)

is close to line

AC

, the gradient condition for collinearity is "approximately satisfied", so

A

B

C

D

are "approximately collinear". Justify why this reasoning is mathematically invalid, referring to the exact gradient values in your answer. [3]

Solutions

Questions 5-203

Unlock these questions with Premium

That's every free question here — 4 of 203.

+199 more questions, plus Mock Papers & Worksheets, are waiting in Premium.

Upgrade