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Math Help - Coordinate geometry question

  1. #1
    Junior Member
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    Coordinate geometry question

    This is the question I am stuck on:

    A ramp is placed so it rises 2 m vertically with the top end 15m from the start of the ramp represented by (0,0). The ramp has two concrete supports, both positioned on level ground.

    I figured out that the length of the ramp is 15.13m and the gradient is 0.13 and the angle is 7.59. These are correct but the following part of the question I am stuck on:

    The position of the support at the end of the ramp can be represented by the equation y= -4x+62. Use this information to find the distance from the botom of the support to the start of the ramp.

    Could someone please help me with this part of the question?
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  2. #2
    MHF Contributor
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    Quote Originally Posted by Paulo1913 View Post
    This is the question I am stuck on:

    A ramp is placed so it rises 2 m vertically with the top end 15m from the start of the ramp represented by (0,0). The ramp has two concrete supports, both positioned on level ground.

    I figured out that the length of the ramp is 15.13m and the gradient is 0.13 and the angle is 7.59. These are correct but the following part of the question I am stuck on:

    The position of the support at the end of the ramp can be represented by the equation y= -4x+62. Use this information to find the distance from the botom of the support to the start of the ramp.

    Could someone please help me with this part of the question?
    I assume the problem meant, for simplicity, that one corner of the start of the ramp is at (0,0) and a corresponding corner of the top of the ramp is at (15,2).
    The said support at the top end follows the equatin y = -4x +62.

    Let's check first if this support really touches the top end of the ramp.
    y = -4x +62
    2 = -4(15) +62
    2 = -60 +62
    2 = 2
    True. So, okay the support really touches the ramp at its top end.

    Now you want to know how far away is the bottom of the support from the start of the ramp. Since the ramp and the support are on level ground, then the bottom of the support should be in the same level of the start, meaning, y=0 also at the bottom of the support.
    So,
    y = -4x +62
    0 = -4x +62
    4x = 62
    x = 62/4 = 15.5

    Therefore, the bottom of the support is at 15.5 meters from the start of the ramp. -----answer.
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