Question

The line I has equation 3x + 4y = 24. It crosses the x-axis at the point A and the y-axis at the point B. Find

(i) the coordinates of A and of B,

(ii) the length of the line segment AB,

(iii) the coordinates of the point C that lies on the line I such that C is equidistant from the coordinate axes,

(iv) the equation of the line OC, where 0 is the origin.​

Answer 1

Answer:

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

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Answer 2

Answer:0

Step-by-step explanation: