find the ratio in which x-axis divides the line segment AB joining the points A(-4,1) and B(1,1) from the side of A
Answers
The ratio in which x axis divide the line segment AB is 1 : 2 and coordinate of point of intersection on x-axis is ( 5 , 0 )
Step-by-step explanation:
Given: Points are A( 2 , -3 ) and B( 5 , 6 )
To find: Ratio when line AB intersected by x - axis
intersecting point on x-axis
let the ratio be k : 1 and the point where line AB intersect x-axis be ( x , 0 )
Section formula is given by,
coordinate\,of\,point=(\frac{m\times x_2+n\times x_1}{m+n},\frac{m\times y_2+n\times y_1}{m+n})coordinateofpoint=(
m+n
m×x
2
+n×x
1
,
m+n
m×y
2
+n×y
1
)
So we get,
coordinate\,of\x-axis=(\frac{k\times5+1\times2}{k+1},\frac{k\times6+1\times(-3)}{k+1})coordinateof\x−axis=(
k+1
k×5+1×2
,
k+1
k×6+1×(−3)
)
(x,0)=(\frac{5k+2}{k+1},\frac{6k-3}{k+1})(x,0)=(
k+1
5k+2
,
k+1
6k−3
)
On comparing y-coordinates we get,
\implies0=\frac{6k-3}{k+1}⟹0=
k+1
6k−3
0=6k-30=6k−3
6k=36k=3
k=\frac{3}{6}k=
6
3
k=\frac{1}{2}k=
2
1
\implies k:1=\frac{1}{2}:1=1:2⟹k:1=
2
1
:1=1:2
put value of k in x-coordinate to get x-coordinate of x-axis,
\implies x=\frac{5\times\frac{1}{2}+2}{\frac{1}{2}+1}⟹x=
2
1
+1
5×
2
1
+2
x=\frac{\frac{5+10}{2}}{\frac{1+2}{2}}x=
2
1+2
2
5+10
x=\frac{\frac{15}{2}}{\frac{3}{2}}x=
2
3
2
15
x=\frac{15}{3}x=
3
15
x = 5
Therefore, The ratio in which x axis divide the line segment AB is 1 : 2 and coordinate of point of intersection on x-axis is ( 5 , 0 )