(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)?

Question

(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)?

KnowledgeBoat · Accepted Answer

(i) Equation of line through (-2, 3) and (4, 1) can be given by two-point form i.e., y - y1 = (x - x1) Substituting values we get, Comparing the above equation with y = mx + c we get, Slope = m1 = The other equation is 3x = y + 1 or y = 3x - 1, comparing this with y = mx + c we get, slope = m2 = 3 Product of slopes, = m1 × m2 = × 3 = -1. Since, the product of slopes is -1 hence, the lines are perpendicular to each other. Hence, the line joining A(–2, 3) and B(4, 1) is perpendicular to the line 3x – y = 1. (ii) Mid-point of (-2, 3) and (4, 1) can be given by mid-point formula i.e., Line 3x = y + 1 bisects the line joining (-2, 3) and (4, 1) if the mid-point i.e., (1, 2) satisfies the equation. Substituting (1, 2) in 3x = y + 1. L.H.S. = 3x = 3(1) = 3. R.H.S. = y + 1 = 2 + 1 = 3. Since, L.H.S. = R.H.S. hence, (1, 2) satisfies 3x = y + 1. Hence, the line 3x – y = 1 bisects the join of A(–2, 3) and B(4, 1).

Mathematics

(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)?

Straight Line Eq

Related Questions

A(1, 2), B(2, 3) and C(4, 3) are the vertices of a ΔABC. Find :
(i) the equation of altitude through B
(ii) the equation of altitude through C
(iii) the co-ordinates of the orthocentre of ΔABC

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

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.

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.

Mathematics

(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)?

Straight Line Eq

Related Questions

A(1, 2), B(2, 3) and C(4, 3) are the vertices of a ΔABC. Find :(i) the equation of altitude through B(ii) the equation of altitude through C(iii) the co-ordinates of the orthocentre of ΔABC

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

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.

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.

(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)?

A(1, 2), B(2, 3) and C(4, 3) are the vertices of a ΔABC. Find :
(i) the equation of altitude through B
(ii) the equation of altitude through C
(iii) the co-ordinates of the orthocentre of ΔABC

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

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.

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.