find the ratio in which the line segment joining the points (6 4) and (1 –7) is divided by x-axis
Answers
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Answer:
The ratio is 4 :7.
The coordinate of point of division is (\frac{46}{11},0)(
11
46
,0)
Step-by-step explanation:
Given : Line segment joining the points (6,4)and(1,-7) is divided by x axis.
To find : The ratio in the line segment and the coordinates of point of division?
Solution :
Let the line segment points A=(6,4) and B=(1,-7)
Let the line segment divide by x-axis with point P=(x,0)
Let the ratio in which line segment divide be m:n=k : 1
Applying section formula,
(x,y)=(\frac{a_2m+a_1n}{m+n}, \frac{b_2m+b_1n}{m+n})(x,y)=(
m+n
a
2
m+a
1
n
,
m+n
b
2
m+b
1
n
)
a_1=6,b_1=4,a_2=1,b_2=-7,m=k,n=1a
1
=6,b
1
=4,a
2
=1,b
2
=−7,m=k,n=1
Substitute the values,
(x,0)=(\frac{1(k)+6(1)}{k+1}, \frac{-7(k)+4(1)}{k+1})(x,0)=(
k+1
1(k)+6(1)
,
k+1
−7(k)+4(1)
)
(x,0)=(\frac{k+6}{k+1}, \frac{-7k+4}{k+1})(x,0)=(
k+1
k+6
,
k+1
−7k+4
)
Compare the y-coordinate,
\frac{-7k+4}{k+1}=0
k+1
−7k+4
=0
-7k+4=0−7k+4=0
7k=47k=4
k=\frac{4}{7}k=
7
4
So, The ratio is 4 :7.
Compare the x-coordinate,
\frac{k+6}{k+1}=x
k+1
k+6
=x
Put the value of k,
x=\frac{(\frac{4}{7})+6}{(\frac{4}{7})+1}x=
(
7
4
)+1
(
7
4
)+6
x=\frac{\frac{46}{7}}{\frac{11}{7}}x=
7
11
7
46
x=\frac{46}{11}x=
11
46
So, The coordinate of point of division is (\frac{46}{11},0)(
11
46
,0)
Step-by-step explanation:
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