Question

In what ratio does the x axis divide the line segment joining a (5, 6) and b (2, -8)

Answer 1

The ratio in which x axis divide the line segment joining a (5, 6) and b (2, -8)is 6:8

Step-by-step explanation:

$a=(x_1,y_1)=(5,6)$

$b=(x_2,y_2)=(2,-8)$

We are given that x axis divides the line ab , so y=0

So, the point at which x axis cut the line ab = (x,0)

Let the ratio be k:1

(x,y)=(x,0)

we will use section formula :

$x=\frac{mx_2+nx_1}{m+n} , y=\frac{my_2+ny_1}{m+n}$

Substitute the values

m:n = k :1

$x=\frac{k(2)+1(5)}{k+1} , 0=\frac{k(-8)+1(6)}{k+1}$

$0=\frac{k(-8)+1(6)}{k+1}$

$0=-8k+6$

$8k=6$

$k=\frac{6}{8}$

Hence the ratio in which x axis divide the line segment joining a (5, 6) and b (2, -8)is 6:8

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