Find the coordinates of the point on y-axis which is nearest to the point (–2, 5).

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Question 4 Find the coordinates of the point on y-axis which is nearest to the point (–2, 5). Let A(–2, 5) Since the required point is in y-axis, its x –coordinate will be zero Let Required point = B (0, a) We need to find coordinates of point B such that distance AB is minimum Finding AB Finding AB x1 = –2 , y1 = 5 x2 = 0 , y2 = a AB = √((𝑥2 −𝑥1)2+(𝑦2 −𝑦1)2) = √(( 0 −(−2))2+(𝑎−5)2) = √((2)2+(𝑎 −5)2) = √((6)2+(𝑎 −5)2) Now, AB is least when a – 5 = 0 i.e. a = 5 So, coordinate of required point = (0, 5)

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