B(-5, 6) and D(1, 4) are the vertices of rhombus ABCD. Find the equations of diagonals BD and AC.

The rhombus ABCD is shown in the figure below: By formula, Slope = Substituting values we get, Equation of BD by point-slope form, ⇒ y - y 1 = m(x - x 1 ) ⇒ y - 6 = [x - (-5)] ⇒ 3(y - 6) = -1(x + 5) ⇒ 3y - 18 = -x - 5 ⇒ 3y + x - 18 + 5 = 0 ⇒ x + 3y - 13 = 0 ⇒ x + 3y = 13. Since, diagonals of rhombus are perpendicular to each other. So, product of their slopes will be -1. Slope of AC × Slope of BD = -1 = -1 Slope of AC = -1 × -3 = 3. We know that, Diagonals of rhombus bisect each other. Let diagonals meet at point O. ∴ Mid-point of AC = Mid-point of BD. Co-ordinates of mid-point of BD (i.e. O) = = (-2, 5). ∴ Co-ordinates of mid-point of AC = (-2, 5). Equation of AC by point-slope form, ⇒ y - y 1 = m(x - x 1 ) ⇒ y - 5 = 3[x - (-2)] ⇒ y - 5 = 3[x + 2] ⇒ y - 5 = 3x + 6 ⇒ 3x - y + 6 + 5 = 0 ⇒ 3x - y + 11 = 0 ⇒ y = 3x + 11. Hence, equation of BD is x + 3y = 13 and equation of AC is y = 3x + 11.

Find the equation of the line passing through (-2, 1) and perpendicular to 4x + 5y = 6.

View Answer Bookmark Now

Find the equation of the perpendicular bisector of the line segment obtained on joining the points (6, -3) and (0, 3).

View Answer Bookmark Now

A(1, -5), B(2, 2) and C(-2, 4) are the vertices of triangle ABC. Find the equation of :
(i) the median of the triangle through A.
(ii) the altitude of the triangle through B.
(iii) the line through C and parallel to AB.

View Answer Bookmark Now

(i) Write down the equation of the line AB, through (3, 2) and perpendicular to the line 2y = 3x + 5.
(ii) AB meets the x-axis at A and the y-axis at B. Write down the co-ordinates of A and B. Calculate the area of triangle OAB, where O is the origin.

View Answer Bookmark Now

Mathematics

B(-5, 6) and D(1, 4) are the vertices of rhombus ABCD. Find the equations of diagonals BD and AC.

Straight Line Eq

Related Questions

Find the equation of the line passing through (-2, 1) and perpendicular to 4x + 5y = 6.

Find the equation of the perpendicular bisector of the line segment obtained on joining the points (6, -3) and (0, 3).

A(1, -5), B(2, 2) and C(-2, 4) are the vertices of triangle ABC. Find the equation of :
(i) the median of the triangle through A.
(ii) the altitude of the triangle through B.
(iii) the line through C and parallel to AB.

(i) Write down the equation of the line AB, through (3, 2) and perpendicular to the line 2y = 3x + 5.
(ii) AB meets the x-axis at A and the y-axis at B. Write down the co-ordinates of A and B. Calculate the area of triangle OAB, where O is the origin.

Mathematics

B(-5, 6) and D(1, 4) are the vertices of rhombus ABCD. Find the equations of diagonals BD and AC.

Straight Line Eq

Related Questions

Find the equation of the line passing through (-2, 1) and perpendicular to 4x + 5y = 6.

Find the equation of the perpendicular bisector of the line segment obtained on joining the points (6, -3) and (0, 3).

A(1, -5), B(2, 2) and C(-2, 4) are the vertices of triangle ABC. Find the equation of :(i) the median of the triangle through A.(ii) the altitude of the triangle through B.(iii) the line through C and parallel to AB.

(i) Write down the equation of the line AB, through (3, 2) and perpendicular to the line 2y = 3x + 5.(ii) AB meets the x-axis at A and the y-axis at B. Write down the co-ordinates of A and B. Calculate the area of triangle OAB, where O is the origin.

A(1, -5), B(2, 2) and C(-2, 4) are the vertices of triangle ABC. Find the equation of :
(i) the median of the triangle through A.
(ii) the altitude of the triangle through B.
(iii) the line through C and parallel to AB.

(i) Write down the equation of the line AB, through (3, 2) and perpendicular to the line 2y = 3x + 5.
(ii) AB meets the x-axis at A and the y-axis at B. Write down the co-ordinates of A and B. Calculate the area of triangle OAB, where O is the origin.