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    Coordinate Geometry Key Points

    Uploaded by

    Aabidah Ali

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    © All Rights Reserved
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    Coordinate Geometry Key Points

    Uploaded by

    Aabidah Ali
    7 views2 pages

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    7 views2 pages

    Coordinate Geometry Key Points

    Uploaded by

    Aabidah Ali

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 2

    COORDINATE GEOMETRY REVIEW

    In coordinate geometry we use graphs and coordinates to find measurements and other
    useful information about geometric figures. We will be focusing on coordinate geometry as
    it applies to straight lines.

    Remember: points are described using ordered pairs (x, y)

    CONCEPTS COVERED:

    1. Midpoint of a line segment - this is the POINT that is halfway between two given points.

    𝑥! + 𝑥" 𝑦! + 𝑦"
    • What is the formula for midpoint? ! , '
    2 2
    2. Length of a line segment – this is the distance between two endpoints.

    • What is the formula for length of a line? ((𝑦" − 𝑦! )" + (𝑥" − 𝑥! )"

    3. Gradient of a line – this is a NUMBER that describes the slope of a line (how slanted the line may be)
    𝑦" − 𝑦!
    What is the formula for gradient? 𝑚=
    𝑥" − 𝑥!
    What is the gradient of a horizontal line? 𝑚=0

    What is the gradient of a vertical line? 𝑚 𝑖𝑠 𝑖𝑛𝑓𝑖𝑛𝑖𝑡𝑒 𝑜𝑟 𝑢𝑛𝑑𝑒𝑓𝑖𝑛𝑒𝑑

    What is the gradient of an upward sloping line? 𝑚 𝑖𝑠 𝑝𝑜𝑠𝑖𝑡𝑖𝑣𝑒

    What is the gradient of a downward sloping line? 𝑚 𝑖𝑠 𝑛𝑒𝑔𝑎𝑡𝑖𝑣𝑒

    What is the relationship between the gradients of parallel lines? 𝑔𝑟𝑎𝑑𝑖𝑒𝑛𝑡𝑠 𝑎𝑟𝑒 𝑒𝑞𝑢𝑎𝑙

    What is the relationship between the gradients of perpendicular


    𝑔𝑟𝑎𝑑𝑖𝑒𝑛𝑡𝑠 𝑎𝑟𝑒 𝑛𝑒𝑔𝑎𝑡𝑖𝑣𝑒 𝑟𝑒𝑐𝑖𝑝𝑟𝑜𝑐𝑎𝑙𝑠
    lines?

    4. Intercepts of a straight line – points on a straight line which intersect the x axis and y axis

    What is the equation of the x-axis? 𝑦=0


    What is known about every point that lies on the x-axis? 𝑡ℎ𝑒 𝑦 𝑐𝑜𝑜𝑟𝑑𝑖𝑛𝑎𝑡𝑒 𝑖𝑠 𝑎𝑙𝑤𝑎𝑦𝑠 0

    What is the equation of the y-axis? 𝑥=0

    What is known about every point that lies on the y-axis? 𝑡ℎ𝑒 𝑥 𝑐𝑜𝑜𝑟𝑑𝑖𝑛𝑎𝑡𝑒 𝑖𝑠 𝑎𝑙𝑤𝑎𝑦𝑠 0

    5. Equation of a straight line – an equation which describes the relationship between the coordinates
    of points on a given line

    What is the general form of the equation of a diagonal straight


    𝑦 = 𝑚𝑥 + 𝑐
    line?

    What are the two values you need to know to determine the 𝑔𝑟𝑎𝑑𝑖𝑒𝑛𝑡 (𝑚) 𝑎𝑛𝑑
    equation of a straight line? 𝑦 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 (𝑐)

    What is the general form of the equation of a horizontal line? 𝑦 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡

    What is the general form of the equation of a vertical line? 𝑥 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡

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