Question

5. Find the ratio in which the line segment joining A(1,-5) and B(-4,5) is divided
x-axis. Also find the coordinates of the point of division.​

Answer 1

Step-by-step explanation:

Solution :

Let the line AB divides by Point C in a ration k:1

Then, Using section formula

(x_3,y_3)=\frac{x_1n+x_2m}{m+n},\frac{y_1n+y_2m}{m+n}(x

3

,y

3

)=

m+n

x

1

n+x

2

m

,

m+n

y

1

n+y

2

m

Divided by the x-axis.

So, y_3=\frac{y_1n+y_2m}{m+n}y

3

=

m+n

y

1

n+y

2

m

0=\frac{(-5)(1)+5k}{k+1}0=

k+1

(−5)(1)+5k

-5+5k=0−5+5k=0

5=5k5=5k

k=\farc{5}{5}k=\farc55

k=1k=1

Which means x axis will divide the line segment AB in a ratio 1:1, externally.

Therefore, The ratio is 1:1.

Now, to find x-coordinate,

x_3=\frac{x_1n+x_2m}{m+n}x

3

=

m+n

x

1

n+x

2

m

x_3=\frac{1(1)+(-4)(1)}{1+1}x

3

=

1+1

1(1)+(−4)(1)

x_3=\frac{1-4}{2}x

3

=

2

1−4

x_3=\frac{-3}{2}x

3

=

2

−3

Therefore, x-coordinate is \frac{-3}{2}

2

−3

Answer 2

ans ratio 1:1

(-3/2,0) the point