Question

Ques 4 : The equation of line l is 3x –4y = 24. The line intersects the x-axis at A and the y-axis at
B. Find
a) The coordinates of A and B points
b) The coordinates of the midpoint M
c) Find the equation of line parallel to AB and passes through the point(4,9)
show answer in a written form

Answer 1

Step-by-step explanation:

As the point A lies on the x - axis, its y coordinate =0.

To find the co-ordinates of the point A, substitute y=0 in the equation of the line 3x−4y+12=0.

Hence, 3x−4(0)+12=0.

=>3x=−12

=>x=−4

So, point A =(−4,0)

Similarly, as the point B lies on the y - axis, its x coordinate =0.

To find the co-ordinates of the point B, substitute x=0 in the equation of the line 3x−4y+12=0.

Hence, 3(0)−4y+12=0.

=>4y=12

=>y=3

So, point B =(0,3)

Formula to calculate distance between two points (x

1

,y

1

) and (x

2

,y

2

)=

(x

2

−x

1

)

2

+(y

2

−y

1

)

2

So, length of AB=

(0−(−4))

2

+(3−0)

2

=

16+9

=

25

=5