Question

The slope of the line determined by the equation 3 − 2 = −4 is 3
2

Answer 1

Equation of line with given slope

4

3

and from point A(3,2)

y−2=

4

3

(x−3)

4y−8=3x−9

3x=1+4y------(1)

Let Point B(x

1

,y

1

)

The distance between A and B is 5 Hence by distance formula

(x

1

−3)

2

+(y

1

−2)

2

=25

x

1

2

+9−6x

1

+y

1

2

+4−4y

1

=25

x

1

2

+y

1

2

−6x

1

−4y

1

−12=

Point B lies on line 3x=1+4y

Hence x

1

=

3

4y

1

+1

(

3

4y

1

+1

)

2

+y

1

2

−6(

3

4y

1

+1

)−4y

1

−12=0

9

16y

1

2

+1+8y

1

+y

1

2

−8y

1

−2−4y

1

−12=0

16y

1

2

+1+8y

1

+9y

1

2

−72y

1

−18−36y

1

−108=0

25y

1

2

−100y

1

−125=0

y

1

2

−4y

1

−5=0

y

1

2

−5y

1

+y

1

−5=0

(y

1

−5)(y

1

+1)=0

⇒y

1

=−1,5

From equation (1)

3x

1

=1+4y

1

3x

1

=1−4 and 3x

1

=1+20

x

1

=−1 and x

1

=7

Point B(7,5) and (−1,−1)