In what ratio is the segment joining (12,−1) and (−3,4) divided by the Y-axis?
- A4:1
- B1:4
- C4:3
- D3:4
Solution & Step-by-step Explanation
Let the Y-axis divide the line segment joining the points A(12,−1) and B(−3,4) in the ratio k:1.
Any point lying on the Y-axis has its x-coordinate equal to 0, i.e., (0,y).
By using the section formula, the x-coordinate of the dividing point is given by:
x=
k+1
k⋅x
2
+1⋅x
1
Here, x
1
=12 and x
2
=−3. Setting x=0:
0=
k+1
k(−3)+1(12)
0=−3k+12
3k=12
k=4
So, the ratio k:1 is 4:1.
Any point lying on the Y-axis has its x-coordinate equal to 0, i.e., (0,y).
By using the section formula, the x-coordinate of the dividing point is given by:
x=
k+1
k⋅x
2
+1⋅x
1
Here, x
1
=12 and x
2
=−3. Setting x=0:
0=
k+1
k(−3)+1(12)
0=−3k+12
3k=12
k=4
So, the ratio k:1 is 4:1.