Q. 225.0( 8 Votes )
P (a, b) is the mid-point of a line segment between axes. Show that equation of the line is
.
Answer :
Let AB be a line segment whose midpoint is P (a, b).
Let the coordinates of A and B be (0, y) and (x, 0) respectively.
We know that the midpoint formula is given by .
Since P is the midpoint of (a, b),
⇒
⇒ a = x/2 and b = y/2
⇒ x = 2a and y = 2b
∴ A = (0, 2b) and B = (2a, 0)
We know that the equation of the line passing through the points (x1, y1) and (x2, y2) is given by
∴
⇒
⇒
⇒ a (y – 2b) = -bx
⇒ ay – 2ab = -bx
⇒ bx + ay = 2ab
Dividing by ab on both sides,
⇒
⇒
Ans. The equation of line is .
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