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Distance of a point from a line measured parallel to another line

This type of question, asked 2 times: 29 Jan 2024, 31 Jan 2024. All 2 questions below, oldest first.

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  1. Question 1

    29 Jan 2024

    161
    The distance of the point (2,3)(2,3) from the line 2x−3y+28=02x-3y+ 28 = 0, measured parallel to the line 3x−y+1=0\sqrt{3}x-y+ 1 = 0, is equal to

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  2. Question 2

    31 Jan 2024

    152
    Let A(a,b),B(3,4)A(a,b),B(3,4) and (−6,−8)( - 6, - 8) respectively denote the centroid, circumcentre and orthocentre of a triangle. Then, the distance of the point P(2a+3,7 b+5)P(2a + 3,7\text{ }b + 5) from the line 2x+3y−4=02x + 3y - 4 = 0 measured parallel to the line x−2y−1=0x - 2y - 1 = 0 is

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