A straight line passes through the point (3, 2) and the portion of this line, intercepted between the positive axes, is bisected at this point. Find the equation of the line.
Straight Line Eq
22 Likes

Question

A straight line passes through the point (3, 2) and the portion of this line, intercepted between the positive axes, is bisected at this point. Find the equation of the line.

KnowledgeBoat · Accepted Answer

Let P = (3, 2). Let the line intersect the x-axis at point A (x, 0) and y-axis at point B (0, y). Since, P is the mid-point of AB, we have: Thus, A = (6, 0) and B = (0, 4) Slope of line AB = . So, the required equation of the line AB is given by ⇒ y – y₁ = m(x – x₁) ⇒ y – 0 = (x – 6) ⇒ 3y = -2x + 12 ⇒ 2x + 3y = 12 Hence, equation of the required line is 2x + 3y = 12.

Mathematics

A straight line passes through the point (3, 2) and the portion of this line, intercepted between the positive axes, is bisected at this point. Find the equation of the line.

Straight Line Eq

Related Questions

Show that A (3, 2), B (6, -2) and C (2, -5) can be the vertices of a square.
(i) Find the co-ordinates of its fourth vertex D, if ABCD is a square.
(ii) Without using the co-ordinates of vertex D, find the equation of side AD of the square and also the equation of diagonal BD.

A line through origin meets the line x = 3y + 2 at right angles at point X. Find the co-ordinates of X.

Find the equation of the line passing through the point of intersection of 7x + 6y = 71 and 5x – 8y = -23; and perpendicular to the line 4x – 2y = 1.

Determine whether the line through points (-2, 3) and (4, 1) is perpendicular to the line 3x = y + 1.
Does the line 3x = y + 1 bisect the line segment joining the two given points?

Mathematics

A straight line passes through the point (3, 2) and the portion of this line, intercepted between the positive axes, is bisected at this point. Find the equation of the line.

Straight Line Eq

Related Questions

Show that A (3, 2), B (6, -2) and C (2, -5) can be the vertices of a square.(i) Find the co-ordinates of its fourth vertex D, if ABCD is a square.(ii) Without using the co-ordinates of vertex D, find the equation of side AD of the square and also the equation of diagonal BD.

A line through origin meets the line x = 3y + 2 at right angles at point X. Find the co-ordinates of X.

Find the equation of the line passing through the point of intersection of 7x + 6y = 71 and 5x – 8y = -23; and perpendicular to the line 4x – 2y = 1.

Determine whether the line through points (-2, 3) and (4, 1) is perpendicular to the line 3x = y + 1.Does the line 3x = y + 1 bisect the line segment joining the two given points?

Show that A (3, 2), B (6, -2) and C (2, -5) can be the vertices of a square.
(i) Find the co-ordinates of its fourth vertex D, if ABCD is a square.
(ii) Without using the co-ordinates of vertex D, find the equation of side AD of the square and also the equation of diagonal BD.

Determine whether the line through points (-2, 3) and (4, 1) is perpendicular to the line 3x = y + 1.
Does the line 3x = y + 1 bisect the line segment joining the two given points?