Find the ratio in which the line joining (3,4) and (-4,7) is divided by y-axis. Also find the coordinates of the point of intersection
Answers
Let the ratio be k:1
A(3,4) ; B(-4,7) ; Y(0,y)
x=M2X1+M1X2/M1+M2
x=1(3)+k(-4)/k+1
x=0
0=3-4k/k+1
0(k+1)=3-4k
0=3-4k
4k=3
k=3/4
y=M2Y1+M1Y2/M1+M2
y=1(4)+k(7)/k+1 ...(1)
putting k=3/4 in (1)
y=4+7(3/4)/3/4+1
y=16+21/4/3+4/4
y=37/7=5.28
Hence,the ratio in which the line joining is divided by y-axis is 3:4. And, the coordinate of point of intersect is (0,5.28)
Answer: The ratio in which the line is divided by the y-axis is 4/3 and the coordinates of the point of intersection are (0, 5/3).
To find the ratio in which the line joining (3,4) and (-4,7) is divided by the y-axis, we can use the section formula:
Let the coordinates of the point of intersection be (0, y).
Then, the ratio in which the line is divided by the y-axis is:
(-4 - 0) / (3 - 0) = -4/3
So, The ratio in which the line joining (3,4) and (-4,7) is divided by the y-axis is 4:3.
The negative sign in the ratio indicates that the point of intersection lies on the opposite side of the y-axis from the point (3, 4).
Simplifying the equation, we get:
3(7 - y) = 16
21 - 3y = 16
3y = 5
y = 5/3
Therefore, the coordinates of the point of intersection are (0, 5/3) and the line joining (3,4) and (-4,7) is divided by the y-axis in the ratio of 4:3.
Learn more about ratios here
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Learn more about point of intersection here
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