Question

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

Answer 1

Coordinates of the mid point X on the line joining of the points A and B are:

X= [( x1+x2)/2 ,( y1+y2)/2 ] ( midpoint Formula)

Since (1,p/3) is the midpoint of the line segment joining the points (2,0) & (0,2/9)

Here,
x= 1, y= p/3 , x1= 2, y1= 0 , x2= 0 , y2= 2/9

y= (y1+y2)/2

p/3=( 0+2/9)/2

p/3= (2/9)/2

2p =( 2/9)× 3

p = 3/9

p = ⅓

Given : (-1,3p)

x= -1 , y= 3p

y= 3× ⅓

y = 1

5x+3y+2=0. (Given)

Put the value of x & y

5 (-1) + 3(1)+2= 0

-5+3+2= 0

-2+2= 0

Hence, The line 5x + 3y + 2 = 0 passes through the point (–1, 1) as 5(–1) + 3(1) + 2 = 0.

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Hope this will help you...

Answer 2

SINCE

(1,P/3) IS THE MID POINT OF THE LINE SEGMENT JOINING THE POINTS (2,0) AND (0,2/9)

THEREFORE : P/3 = 0+2/9

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2

P = 1/3

THEREFORE : 5x + 3y + 2 =0

PUT x = -1 and y = 3p = 3 × 1/3 = 1

THEREFORE : 5 (-1) + 3 (1) + 2 =0

Since the points satisfy the equation the line passes through the point (-1,3p)