Find the value of k such that the line (k – 2)x + (k + 3)y – 5 = 0 is: (i) perpendicular to the line 2x – y + 7 = 0 (ii) parallel to it.

Given line equation, ⇒ 2x - y + 7 = 0 ..........(1) ⇒ y = 2x + 7 Comparing above equation with y = mx + c we get, Slope (m 1 ) = 2 Given line equation, ⇒ (k - 2)x + (k + 3)y - 5 = 0 ..........(2) ⇒ (k + 3)y = -(k - 2)x + 5 ⇒ y = Comparing above equation with y = mx + c we get, Slope (m 2 ) = (i) If lines (1) and (2) are perpendicular then product of their slopes = -1. ⇒ m 1 x m 2 = -1 Hence, k = 7. (ii) If lines 1 and 2 are parallel then their slopes will be equal. ⇒ = 2 ⇒ -(k - 2) = 2(k + 3) ⇒ -k + 2 = 2k + 6 ⇒ 2k + k = 2 - 6 ⇒ 3k = -4 ⇒ k = . Hence, k = .

Given a straight line x cos 30° + y sin 30° = 2. Determine the equation of the other line which is parallel to it and passes through (4, 3).

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From the given figure, find:
(i) the co-ordinates of A, B and C.
(ii) the equation of the line through A and parallel to BC.

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The vertices of a triangle ABC are A (0, 5), B (-1, -2) and C (11, 7). Write down the equation of BC. Find :
(i) the equation of line through A and perpendicular to BC.
(ii) the co-ordinates of the point P, where the perpendicular through A, as obtained in (i), meets BC.

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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?

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Mathematics

Find the value of k such that the line (k – 2)x + (k + 3)y – 5 = 0 is:
(i) perpendicular to the line 2x – y + 7 = 0
(ii) parallel to it.

Straight Line Eq

Related Questions

Given a straight line x cos 30° + y sin 30° = 2. Determine the equation of the other line which is parallel to it and passes through (4, 3).

From the given figure, find:
(i) the co-ordinates of A, B and C.
(ii) the equation of the line through A and parallel to BC.

The vertices of a triangle ABC are A (0, 5), B (-1, -2) and C (11, 7). Write down the equation of BC. Find :
(i) the equation of line through A and perpendicular to BC.
(ii) the co-ordinates of the point P, where the perpendicular through A, as obtained in (i), meets BC.

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

Find the value of k such that the line (k – 2)x + (k + 3)y – 5 = 0 is:(i) perpendicular to the line 2x – y + 7 = 0(ii) parallel to it.

Straight Line Eq

Related Questions

Given a straight line x cos 30° + y sin 30° = 2. Determine the equation of the other line which is parallel to it and passes through (4, 3).

From the given figure, find:(i) the co-ordinates of A, B and C.(ii) the equation of the line through A and parallel to BC.

The vertices of a triangle ABC are A (0, 5), B (-1, -2) and C (11, 7). Write down the equation of BC. Find :(i) the equation of line through A and perpendicular to BC.(ii) the co-ordinates of the point P, where the perpendicular through A, as obtained in (i), meets BC.

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?

Find the value of k such that the line (k – 2)x + (k + 3)y – 5 = 0 is:
(i) perpendicular to the line 2x – y + 7 = 0
(ii) parallel to it.

From the given figure, find:
(i) the co-ordinates of A, B and C.
(ii) the equation of the line through A and parallel to BC.

The vertices of a triangle ABC are A (0, 5), B (-1, -2) and C (11, 7). Write down the equation of BC. Find :
(i) the equation of line through A and perpendicular to BC.
(ii) the co-ordinates of the point P, where the perpendicular through A, as obtained in (i), meets BC.

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?