If (1, p/3) is the mid-point of the line segment joining the points (2, 0) and (0, 2/9), then show that the line 5 x + 3 y + 2 = 0 passes through the point (–1, 3p).

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Question 10 If (1, ๐‘/3) is the mid-point of the line segment joining the points (2, 0) and (0, 2/9), then show that the line 5x + 3y + 2 = 0 passes through the point (โ€“1, 3p). Let A(2, 0), B(0, 2/9) and let mid-point be C (1, ๐‘/3) Finding coordinates of C (1, ๐‘/3) = ((2 + 0)/2 , (0 + 2/9)/2) (1, ๐‘/3) = (2/2 ,2/9 ร— 1/2) (1, ๐‘/3) = (1 ,1/9) Comparing y-coordinate ๐‘/3 = 1/9 ๐‘ = 3/9 = ๐Ÿ/๐Ÿ‘ We need to show that line 5x + 3y + 2 = 0 passes through (โ€“1, 3p) Point = (โ€“1, 3p) = (โ€“1, 3 ร— 1/3) = (โ€“1, 1) Putting (โ€“1, 1) in line 5x + 3y + 2 = 0 5(โ€“1) + 3(1) + 2 = 0 โ€“5 + 3 + 2 = 0 โ€“5 + 5 =0 0 = 0 Which is true Hence, (1, p) passes through 5x + 3y + 2 = 0

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