Perplex
Content
  • Exponents & Logarithms
  • Approximations & Error
  • Sequences & Series
  • Matrices
  • Complex Numbers
  • Financial Mathematics
  • Cartesian plane & lines
  • Function Theory
  • Modelling
  • Transformations & asymptotes
  • 2D & 3D Geometry
  • Voronoi Diagrams
  • Trig equations & identities
  • Vectors
  • Graph Theory
  • Probability
  • Descriptive Statistics
  • Bivariate Statistics
  • Distributions & Random Variables
  • Inference & Hypotheses
  • Differentiation
  • Integration
  • Differential Equations
Other
  • Review Videos
  • Blog
  • Landing Page
  • Sign Up
  • Login
  • Perplex
    IB Math AIHL
    /
    Cartesian plane & lines
    /

    Problems

    Edit

    Problem Bank - Cartesian plane & lines

    Access custom-built, exam-style problems for cartesian plane & lines. Each problem has a full solution and mark-scheme, as well as AI grading and support.

    Select a Difficulty:

    4 / 45 problems visible - Upgrade to view all problems

    IB: 7
    41

    !

    0 / 19

    A 12km×12km nature reserve uses three rain gauges:

    Gauge

    Coordinates (km)

    Daily rainfall (mm)

    G1​

    (3,3)

    10

    G2​

    (9,3)

    15

    G3​

    (6,9)

    12

    1. Show that the bisector of G2​ and G3​ is the line y=21​x+2.25.

      [4]

    A complete Voronoi diagram is drawn of the nature reserve:


    Powered by Desmos

    1. Determine the point P where the three bisectors meet.

      [4]
    2. Hence estimate the rainfall at point P to two decimal places.

      [3]
    3. Calculate the area of each gauge’s Voronoi cell and hence estimate the mean rainfall over the whole reserve. Give your answer to one decimal place.

      [8]
    42

    !

    Plus

    0 / 20

    Upgrade to Plus to solve this problem
    43
    Plus

    0 / 23

    Upgrade to Plus to solve this problem
    44
    Plus

    0 / 17

    Upgrade to Plus to solve this problem

    Ask Plex AI about problem 41

    Get hints, ask questions, and work through this problem step by step