Position Vectors and Displacement
You're viewing free preview questions — 4 questions previewing here — subscribe to unlock 129 more, plus the Full Question Bank, Mock Papers & Worksheets.Upgrade

Position Vectors and Displacement — Free MYP5 Mathematics (Extended) Practice Questions

1QuestionDefinition and Use of Position VectorsAssessment Practice
6 marks~9 minCriterion B
The diagram shows Figures 1, 2 and 3 of a pattern made from dots. In each figure, the dots form an n×nn \times n square with one additional dot placed immediately to the right of the top-right corner dot. Figure 4 has 17 dots.
a
Write down the number of dots in Figure 5. [1]
b
Find a rule for the number of dots DD in Figure nn, in the form
D=an2+b,D = an^2 + b,
where aa and bb are integers to be found. [2]
c
Verify your rule for Figure 3, and justify why the rule must contain an n2n^2 term by referring to the structure of the pattern. [3]
Question diagram

Solutions

2QuestionDefinition and Use of Position VectorsAssessment Practice
6 marks~9 minCriterion C
The diagram shows a coordinate grid with three vertices of a parallelogram ABCDABCD, where A=(1,2)A = (1, 2), B=(4,3)B = (4, 3), and C=(6,7)C = (6, 7).
a
Find the coordinates of the fourth vertex DD, using the property that the diagonals of a parallelogram bisect each other. [2]
b
Show that the midpoints of diagonals ACAC and BDBD coincide, and state the coordinates of the common midpoint MM. [2]
c
A student claims: "The common midpoint MM is equidistant from all four vertices AA, BB, CC, and DD."

Justify whether this claim is correct by calculating the exact distances MAMA, MCMC, MBMB, and MDMD, and comparing them. [2]
Question diagram

Solutions

3QuestionDefinition and Use of Position VectorsAssessment Practice
6 marks~9 minCriterion A
Points P(3, 4)P(3,\, 4) and Q(−1, 7)Q(-1,\, 7) are shown in the diagram.
a
Write down the distance OPOP, where OO is the origin. [1]
b
Find the coordinates of the midpoint MM of PQPQ, and hence calculate the exact distance OMOM. [3]
c
Point RR lies on segment PQPQ such that PR:RQ=1:2PR : RQ = 1 : 2. Determine the coordinates of RR, then justify whether OO, RR, and MM are collinear. [2]
Question diagram

Solutions

4QuestionDefinition and Use of Position VectorsAssessment Practice
8 marks~12 minCriterion D
A drone delivery company plans routes on a coordinate grid where each unit represents 1 km. The launch point is at the origin O(0,0)O(0, 0). Waypoint AA is at coordinates (3,4)(3, 4) and waypoint BB is at coordinates (7,1)(7, 1).

The diagram shows the positions of OO, AA and BB and the two-leg route O→A→BO \to A \to B.

The company models energy cost as proportional to total distance flown and charges customers 12 USD per km.
a
Calculate the total distance flown along the two-leg route O→A→BO \to A \to B. Give your answer in km. [2]
b
Find the percentage saving in distance if the direct route O→BO \to B is used instead of the two-leg route. Give your answer to 3 significant figures. [3]
c
The straight-line distance from OO to BB is 50\sqrt{50} km. A rival company claims that flying the direct route always gives the shortest possible path between two points and should therefore always be used as a flight-planning rule. Assess whether this claim should be adopted as a general flight-planning rule, supporting your answer with both a mathematical argument and one real-world consideration. [3]
Question diagram

Solutions

Questions 5-133

Unlock these questions with Premium

Sign Up →

That's every free question here — 4 of 133.

+129 more questions, plus Mock Papers & Worksheets, are waiting in Premium.

Upgrade