Question

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

Answer 1

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

use section formula of midpoint .
e.g., $\boxed{\bf{\left(\frac{x_1+x_2}{2}\right),\left(\frac{y_1+y_2}{2}\right)}}$

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

p/3 = 2/18 = 1/9

p = 1/3

now, we have to show that line 5x +3y+2=0passes through the point (-1,3p) or, (-1,3×1/3) or (-1,1)

put x = -1 and y = 1 in line 5x + 3y + 2 = 0

5 × -1 + 3 × 1 + 2 = -5 + 3 + 2 = 0

LHS = RHS

hence, proved