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 
.
Rate this question :
Various Forms of Equations of line45 mins
Parametric Equations of Straight line48 mins
Slope, inclination and angle between two lines48 mins
Interactive Quiz on Equations of line23 mins
Straight line | Analyse your learning through quiz56 mins
General Equation of a line43 mins
Motion in a Straight Line - 0665 mins
Motion in a Straight Line - 0556 mins
Motion in a Straight Line - 0372 mins
Understand The Interesting Concept Of Relative velocity in 1- Dimension44 mins
Find all the points on the line x + y = 4 that lie at a unit distance from the line 4x+3y=10.
RS Aggarwal - MathematicsThe distance between the orthocenter and circumcentre of the triangle with vertices (1, 2) (2, 1) and 
is
What are the points on the x-axis whose perpendicular distance from the line 
is 4 units?
Find the equation of a line for which
p = 8, α = 225°
RD Sharma - MathematicsFind the equation of a line for which
p = 4, α = 150°
RD Sharma - MathematicsArea of the triangle formed by the points ((a + 3)(a + 4), a + 3), ((a + 2)(a + 3), (a + 2)) and ((a + 1)(a + 2), (a + 1)) is
RD Sharma - MathematicsFind the equation of straight line passing through ( – 2, – 7) and having an intercept of length 3 between the straight lines 4x + 3y = 12 and 4x + 3y = 3.
RD Sharma - MathematicsFind the distance of the line 2x + y = 3 from the point ( – 1, – 3) in the direction of the line whose slope is 1.
RD Sharma - Mathematics