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Points on a given line at a given distance from another line

This type of question, asked 3 times: 12 May 2024 S1, 13 May 2026 S2, 15 May 2026 S1. All 3 questions below, oldest first.

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  1. Question 1

    12 May 2024 S1

    114
    The co-ordinates of the points on the line 2x−y=52x-y=5 which are the distance of 1 unit from the line 3x+4y=53x+4y=5 are

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  2. Question 2

    13 May 2026 S2

    59
    The points on the line x+y−4=0x + y - 4 = 0 which are at one unit distance from the line 4x+3y−10=04x + 3y - 10 = 0 are...

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  3. Question 3

    15 May 2026 S1

    56
    The sum of the ordinates of the points on the line 4x+3y=104x + 3y = 10 whose distance from the line x+y−4=0x + y - 4 = 0 is 2\sqrt{2} is equal to ...

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