Find the equation of the line that is perpendicular to 3x + 2y - 8 = 0 and passes through the mid-point of the line segment joining the points (5, -2) and (2, 2).
Straight Line Eq
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Question

Find the equation of the line that is perpendicular to 3x + 2y - 8 = 0 and passes through the mid-point of the line segment joining the points (5, -2) and (2, 2).

KnowledgeBoat · Accepted Answer

Given equation of line, ⇒ 3x + 2y - 8 = 0 Converting it in the form y = mx + c, ⇒ 2y = -3x + 8 ⇒ y = Comparing with y = mx + c we get, Slope (m₁) = Now, the coordinates of the mid-point of the line segment joining the points (5, -2) and (2, 2) will be Let's consider the slope of the line perpendicular to the given line be m₂. Then, The equation of the new line with slope m₂ and passing through can be given by point-slope form i.e., y - y₁ = m(x - x₁) Putting values we get, Hence, the equation of the line is 2x - 3y - 7 = 0.

Mathematics

Find the equation of the line that is perpendicular to 3x + 2y - 8 = 0 and passes through the mid-point of the line segment joining the points (5, -2) and (2, 2).

Straight Line Eq

Related Questions

(i) The line 4x - 3y + 12 = 0 meets the x-axis at A. Write down the coordinates of A.
(ii) Determine the equation of the line passing through A and perpendicular to 4x - 3y + 12 = 0.

Find the equation of the line that is parallel to 2x + 5y - 7 = 0 and passes through the mid-point of the line segment joining the points (2, 7) and (-4, 1).

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Line AB is perpendicular to line CD. Coordinates of B, C and D are (4, 0), (0, -1) and (4, 3) respectively. Find
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Mathematics

Find the equation of the line that is perpendicular to 3x + 2y - 8 = 0 and passes through the mid-point of the line segment joining the points (5, -2) and (2, 2).

Straight Line Eq

Related Questions

(i) The line 4x - 3y + 12 = 0 meets the x-axis at A. Write down the coordinates of A.(ii) Determine the equation of the line passing through A and perpendicular to 4x - 3y + 12 = 0.

Find the equation of the line that is parallel to 2x + 5y - 7 = 0 and passes through the mid-point of the line segment joining the points (2, 7) and (-4, 1).

Find the equation of a straight line passing through the intersection of 2x + 5y - 4 = 0 with x-axis and parallel to the line 3x - 7y + 8 = 0.

Line AB is perpendicular to line CD. Coordinates of B, C and D are (4, 0), (0, -1) and (4, 3) respectively. Find(i) the slope of CD(ii) the equation of line AB

(i) The line 4x - 3y + 12 = 0 meets the x-axis at A. Write down the coordinates of A.
(ii) Determine the equation of the line passing through A and perpendicular to 4x - 3y + 12 = 0.

Line AB is perpendicular to line CD. Coordinates of B, C and D are (4, 0), (0, -1) and (4, 3) respectively. Find
(i) the slope of CD
(ii) the equation of line AB