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    Challengig Coordinate Geometry Exercise

    Uploaded by

    Jenkins CK Tsang
    This document provides 8 coordinate geometry exercises involving finding midpoints, gradients, distances, intersections of lines, solving systems of linear equations to find coordinates of points, sketching regions defined by inequalities, and finding equations of lines and their points of intersection. The exercises require using formulas for midpoint, gradient, distance, solving systems of linear equations, sketching regions defined by inequalities, and finding equations of lines.

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    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd

    Challengig Coordinate Geometry Exercise

    Uploaded by

    Jenkins CK Tsang
    10 views4 pages
    This document provides 8 coordinate geometry exercises involving finding midpoints, gradients, distances, intersections of lines, solving systems of linear equations to find coordinates of points, sketching regions defined by inequalities, and finding equations of lines and their points of intersection. The exercises require using formulas for midpoint, gradient, distance, solving systems of linear equations, sketching regions defined by inequalities, and finding equations of lines.

    Original Description:

    coordinate geometry

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    This document provides 8 coordinate geometry exercises involving finding midpoints, gradients, distances, intersections of lines, solving systems of linear equations to find coordinates of points, sketching regions defined by inequalities, and finding equations of lines and their points of intersection. The exercises require using formulas for midpoint, gradient, distance, solving systems of linear equations, sketching regions defined by inequalities, and finding equations of lines.

    Copyright:

    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd
    Download as docx, pdf, or txt
    10 views4 pages

    Challengig Coordinate Geometry Exercise

    Uploaded by

    Jenkins CK Tsang
    This document provides 8 coordinate geometry exercises involving finding midpoints, gradients, distances, intersections of lines, solving systems of linear equations to find coordinates of points, sketching regions defined by inequalities, and finding equations of lines and their points of intersection. The exercises require using formulas for midpoint, gradient, distance, solving systems of linear equations, sketching regions defined by inequalities, and finding equations of lines.

    Copyright:

    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd
    Download as docx, pdf, or txt
    of 4

    Challenging coordinate geometry exercise

    0)

    Describe how you would find (e.g. what method / formula to use)......

    a)

    The midpoint between 2 points

    b)

    The gradient of a line between 2 points

    c)

    The distance between the points

    d)

    The intersection between 2 lines

    1)
    Let P and Q be (1,3) and (9,13) respectively. Let M and M' be points on the
    same straight line as PQ.
    a)

    Find M such that PM : MQ = 2 : 3

    b)
    Find M' such that PM' : QM' = 2 : 3 (deduce how this question is different from
    (a)?)

    c)
    Find the straight line equation of PQ in the form ax + by + c = 0 where a, b
    and c are integers

    d)

    Find the size of the acute angle between this line and the y-axis.

    e)
    Use 3 inequalities to describe the set of points on or inside the triangle
    formed by the line, the x axis and the y axis.

    2)
    The coordinate of A, B and C are (-1, n), (n, m) and (m, 11). B is the midpoint
    of AC. Find n and m.

    3)
    A (8, 0), B, C and D (-13, -14) lie on the same straight line, with both B and C
    between A and D. It's given that AB : BC = 2 : 1 and BC : CD = 2 : 1 as well. Find
    the coordinates of B and C.

    5)
    a)
    Find k

    It's given that A (2,5), B(4,k) and C(2k, 2) are on the same straight line.

    b)
    It's given that A (2,5), B(4,k) and C(m, 2) are on the same straight line
    such that AB : BC = 5 : 1. Find k and m.

    6)
    Let O = origin and A = (13,0). Find 2 points P and P' on the line y x = 2 such
    that OPA (or OP'A) are right angles.
    Answer. Let the x-coordinate of P (or P') be x. Then the y-coordinate is (in terms of
    x)............................

    7) Sketch the inequalities below and hence find the number of integer-valued
    ordered pairs (x,y) that (a) lie on the boundaries of; (b) lie inside the region defined
    by......
    x+y>4
    y < 0.5x + 4
    y > 2x - 4

    8) OABC is a kite with O = the origin, A = (?, ?), B = (5,10) and C = (1,7)
    a)

    Find the gradient of OB.

    b)
    AC

    The "diagonals" of a kite always crosses at right angles. Find the gradient of

    c)

    Find the equation for AC

    d)

    Find the intersection of OB and AC

    e)

    Hence find the coordinates of A.

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