Question

Q13.
The line segment joining P(5,-2) and Q(9,6) is divided in the ratio 3:1 by a point A on it. Find the equation of a line through the point A perpendicular to the line x-3y+4=0

Answer 1

Step-by-step explanation:

Given that:The line segment joining P (5,-2) and Q(9, 6) is divided in the ratio 3 : 1 by a point A on it Find the equation of a line through the point A perpendicular on the line x-3y +4-0.

To find:Find the equation of a line through the point A perpendicular on the line x-3y +4-0.

Solution:

To find line passing through A,

first find the coordinates of point A by applying section formula

Section formula:

Let Point A(x1,y1) and B(x2,y2) are divided by point C(x,y) in ratio m:n,then coordinates of C are

To find A:The line segment joining P (5,-2) and Q(9, 6) is divided in the ratio 3 : 1 by a point A

Coordinates of A(8,4)

To find line passing through a point

To find slope: Use

Convert this line in slope intercepted form,i. e. y=mx+c

Solve of line x-3y+4=0 is 1/3

Solpe of line perpendicular to x-3y+4=0 is -3.

Solpe of two lines ,if they are perpendicular

Thus,equation of line passing through A(8,4) having slope -3

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