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 MYP5 Mathematics (Extended) Practice Questions

1QuestionClassifying shapes and anglesAssessment Practice
6 marks~9 minCriterion C
The diagram shows triangle ABCABC with AB=10AB = 10 cm, BC=7BC = 7 cm, and ∠BAC=38∘\angle BAC = 38^\circ.
a
State why the given information produces an ambiguous case when applying the sine rule. [1]
b
Find the two possible values of ∠BCA\angle BCA, giving your answers to one decimal place. [2]
c
For each value of ∠BCA\angle BCA found in part (b), find the corresponding length ACAC in centimetres to three significant figures. Justify which value of ACAC is consistent with a surveyor's requirement that the triangle must have an obtuse angle at CC. [3]
Question diagram

Solutions

2QuestionAngles in intersecting and parallel linesAssessment Practice
6 marks~9 minCriterion A
The diagram shows two parallel lines pp and qq cut by a transversal tt. Angle aa, formed between tt and line pp on the right-hand side below pp, measures (3x+15)°(3x + 15)°. Angle bb, in the alternate interior position between tt and line qq, measures (5x−27)°(5x - 27)°. A third line rr passes through the point where tt meets qq. The angle between rr and qq, measured on the same side as bb, equals 13\dfrac{1}{3} of angle aa.
a
State the geometric relationship between angles aa and bb, and hence form an equation in xx. [2]
b
Find the value of xx and calculate the size of angle aa. [2]
c
Justify whether line rr is perpendicular to line tt. [2]
Question diagram

Solutions

3QuestionRotation around a given pointAssessment Practice
7 marks~11 minCriterion B
The diagram shows triangle ABCABC with vertices A(1,2)A(1, 2), B(4,2)B(4, 2), and C(4,5)C(4, 5).

Triangle ABCABC is first rotated 90∘90^\circ clockwise about the origin to give triangle A1B1C1A_1B_1C_1, then reflected in the line y=−xy = -x to give triangle A′B′C′A'B'C'.
a
Find the coordinates of A1A_1, B1B_1, and C1C_1 after the 90∘90^\circ clockwise rotation about the origin. [2]
b
Find the coordinates of A′A', B′B', and C′C' after the reflection in the line y=−xy = -x. [2]
c
Justify that a single transformation maps triangle ABCABC directly onto triangle A′B′C′A'B'C', stating the mirror line and verifying your answer using the coordinates of at least two vertex pairs. [3]
Question diagram

Solutions

4QuestionCoordinate geometry (distance, midpoint, gradient formulas)Assessment Practice
8 marks~12 minCriterion D
A city planner is designing a park on a coordinate grid where 1 unit represents 100 m. Entrance A is at (3,7)(3, 7) and Entrance B is at (15,2)(15, 2). A straight footpath is planned directly between A and B.

The diagram shows the positions of A, B, and the fountain F at (3,2)(3, 2).
a
Show that the straight-line distance between A and B on the grid is exactly 13 units. [2]
b
A second route connects A to the fountain F at (3,2)(3, 2), then continues from F to B. The planner claims this two-segment route is longer than the direct path AB. Determine whether the planner's claim is correct, giving all distances in metres. [2]
c
The straight footpath AB is built. A surveyor measures the actual walking distance as 1 430 m. The percentage error between the planned length and the surveyed distance is given by

percentage error=∣planned−actual∣actual×100%\text{percentage error} = \frac{|\text{planned} - \text{actual}|}{\text{actual}} \times 100\%

Calculate the percentage error to 1 decimal place. Advise the city planner whether the planned length is suitable to use for construction budgeting, justifying your answer with reference to the percentage error. [4]
Question diagram

Solutions

Questions 5-203

Unlock these questions with Premium

Sign Up →

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

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

Upgrade