Question

A line perpendicular to the line segment joining the points A ( 1, 0 ) and B ( 2, 3 ), divides it at C in the ratio of 1 : 3. Then the equation of the line is

Answer 1

Answer:

A line perpendicular to the line segment joining the points A(1,0) and B 2,3),divides it at C in the ratio of 1:3. Then the equation of the line is. 2x+6y−9=0.

Answer 2

Answer:

y = $-\frac{1}{3}$ x + $\frac{7}{6}$

Step-by-step explanation:

1). m = $\frac{y_{2} -y_{1} }{x_{2} -x_{1} }$ ; y - $y_{1}$ = m( x - $x_{1}$ ) ; Slope of perpendicular line is opposite reciprocal to "m" .

2). The coordinates of a point that divides a line segment in the ratio a : b are $(\frac{ax_{2} +bx_{1} }{a+b} , \frac{ay_{2} +by_{1} }{a+b} )$  

~~~~~~~~

1). A (1, 0) and B (2, 3)

$m_{AB}$ = $\frac{3-0}{2-1}$ = 3

y - 0 = 3(x - 1) ⇔ y = 3x - 3

2). The ratio is 1 : 3 ⇒ C $(\frac{2+3}{4} ,\frac{3+0}{4} )$ ⇒ C (5/4 , 3/4)

y - $\frac{3}{4}$ = $-\frac{1}{3}$ ( x - $\frac{5}{4}$ )

y = $-\frac{1}{3}$ x + $\frac{5}{12}$ + $\frac{3}{4}$

y = $-\frac{1}{3}$ x + $\frac{7}{6}$