Find the equation of the perpendicular from the point P(1, –2) on the line 4x – 3y – 5 = 0. Also, find the co-ordinates of the foot of the perpendicular.
Straight Line Eq
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Question

Find the equation of the perpendicular from the point P(1, –2) on the line 4x – 3y – 5 = 0. Also, find the co-ordinates of the foot of the perpendicular.

KnowledgeBoat · Accepted Answer

Solving, ⇒ 4x - 3y - 5 = 0 ⇒ 3y = 4x - 5 ⇒ y = Comparing above equation with y = mx + c we get, Slope of the line (m1) = Let the slope of the line perpendicular to 4x - 3y - 5 = 0 be m2. Then, The equation of the line having slope m2 and passing through the point (1, -2) can be given by point-slope form i.e., ⇒ y - y1 = m(x - x1) ⇒ y - (-2) = ⇒ 4(y + 2) = −3(x − 1) ⇒ 4y + 8 = −3x + 3 ⇒ 3x + 4y + 5 = 0. For finding the coordinates of the foot of the perpendicular which is the point of intersection of the lines. Let point of intersection of lines be Q. 4x - 3y - 5 = 0 .......(1) 3x + 4y + 5 = 0 ........(2) On multiplying equation (1) by 4, we get : 16x - 12y - 20 = 0 ...........(3) On multiplying equation (2) by 3, we get : 9x + 12y + 15 = 0 ..........(4) Adding equations (3) and (4) we get, ⇒ 16x - 12y - 20 + 9x + 12y + 15 = 0 ⇒ 25x - 5 = 0 ⇒ x = ⇒ x = . Substituting value of x in (1), we get : Q = Hence, the equation of the new line is 3x + 4y + 5 = 0 and coordinates of the foot of perpendicular are .

Mathematics

Find the equation of the perpendicular from the point P(1, –2) on the line 4x – 3y – 5 = 0. Also, find the co-ordinates of the foot of the perpendicular.

Straight Line Eq

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