A line segment AB meets x-axis at A and y-axis at B. P(4, –1) divides AB in the ratio 1 : 2.
(i) Find the co-ordinates of A and B.
(ii) Find the equation of the line through P and perpendicular to AB.

Question

A line segment AB meets x-axis at A and y-axis at B. P(4, –1) divides AB in the ratio 1 : 2.
(i) Find the co-ordinates of A and B.
(ii) Find the equation of the line through P and perpendicular to AB.

KnowledgeBoat · Accepted Answer

(i) As A lies on x-axis let its co-ordinates be (a, 0) and B lies on y-axis so, co-ordinates = (0, b). By section-formula, Hence, A = (6, 0) and B = (0, -3). (ii) By formula, Slope of AB = Let slope of perpendicular line be m. Since the product of the slopes of perpendicular lines = -1. ⇒ m × Slope of AB = -1 ⇒ m × = -1 ⇒ m = -2. By point-slope from, Equation of line passing through P and slope = -2 is : ⇒ y - y1 = m(x - x1) ⇒ y - (-1) = -2(x - 4) ⇒ y + 1 = -2x + 8 ⇒ 2x + y = 7. Hence, equation of required line is 2x + y = 7.

Mathematics

A line segment AB meets x-axis at A and y-axis at B. P(4, –1) divides AB in the ratio 1 : 2.
(i) Find the co-ordinates of A and B.
(ii) Find the equation of the line through P and perpendicular to AB.

Straight Line Eq

Related Questions

A(1, 2), B(3, –4) and C(5, –6) are the vertices of ΔABC. Find :
(i) the equation of the right bisector of BC
(ii) the equation of the right bisector of CA
(iii) the co-ordinates of the circumcentre of ΔABC

(i) Is the line passing through the points A(–2, 3) and B(4, 1) perpendicular to the line 3x – y = 1?
(ii) Does the line 3x – y = 1 bisect the join of A(–2, 3) and B(4, 1)?

The vertices of a ΔABC are A(3, 8), B(–1, 2) and C(6, –6). Find :
(i) Slope of BC.
(ii) Equation of a line perpendicular to BC and passing through A.

Line AB is perpendicular to CD. Coordinates of B, C and D are respectively (4, 0), (0, –1) and (4, 3). Find :
(i) Slope of CD.
(ii) Equation of AB.

Mathematics

A line segment AB meets x-axis at A and y-axis at B. P(4, –1) divides AB in the ratio 1 : 2.(i) Find the co-ordinates of A and B.(ii) Find the equation of the line through P and perpendicular to AB.

Straight Line Eq

Related Questions

A(1, 2), B(3, –4) and C(5, –6) are the vertices of ΔABC. Find :(i) the equation of the right bisector of BC(ii) the equation of the right bisector of CA(iii) the co-ordinates of the circumcentre of ΔABC

(i) Is the line passing through the points A(–2, 3) and B(4, 1) perpendicular to the line 3x – y = 1?(ii) Does the line 3x – y = 1 bisect the join of A(–2, 3) and B(4, 1)?

The vertices of a ΔABC are A(3, 8), B(–1, 2) and C(6, –6). Find :(i) Slope of BC.(ii) Equation of a line perpendicular to BC and passing through A.

Line AB is perpendicular to CD. Coordinates of B, C and D are respectively (4, 0), (0, –1) and (4, 3). Find :(i) Slope of CD.(ii) Equation of AB.

A line segment AB meets x-axis at A and y-axis at B. P(4, –1) divides AB in the ratio 1 : 2.
(i) Find the co-ordinates of A and B.
(ii) Find the equation of the line through P and perpendicular to AB.

A(1, 2), B(3, –4) and C(5, –6) are the vertices of ΔABC. Find :
(i) the equation of the right bisector of BC
(ii) the equation of the right bisector of CA
(iii) the co-ordinates of the circumcentre of ΔABC

(i) Is the line passing through the points A(–2, 3) and B(4, 1) perpendicular to the line 3x – y = 1?
(ii) Does the line 3x – y = 1 bisect the join of A(–2, 3) and B(4, 1)?

The vertices of a ΔABC are A(3, 8), B(–1, 2) and C(6, –6). Find :
(i) Slope of BC.
(ii) Equation of a line perpendicular to BC and passing through A.

Line AB is perpendicular to CD. Coordinates of B, C and D are respectively (4, 0), (0, –1) and (4, 3). Find :
(i) Slope of CD.
(ii) Equation of AB.