In what ratio is the line segment joining (2,−4) and (−3,2) divided by the Y-axis?
- A3:2
- B1:3
- C2:3
- D3:1
Solution & Step-by-step Explanation
Let the line segment joining the points A(2,−4) and B(−3,2) be divided by the Y-axis in the ratio k:1 at a point P.
Any point lying on the Y-axis has its x-coordinate equal to 0. Thus, P=(0,y).
Using the section formula, the x-coordinate of the dividing point P is given by:
x=
k+1
k⋅x
2
+1⋅x
1
Here, x
1
=2, x
2
=−3, and x=0.
0=
k+1
k(−3)+1(2)
0=−3k+2
3k=2
k=
3
2
Thus, the ratio k:1 is
3
2
:1, which simplifies to 2:3.
Any point lying on the Y-axis has its x-coordinate equal to 0. Thus, P=(0,y).
Using the section formula, the x-coordinate of the dividing point P is given by:
x=
k+1
k⋅x
2
+1⋅x
1
Here, x
1
=2, x
2
=−3, and x=0.
0=
k+1
k(−3)+1(2)
0=−3k+2
3k=2
k=
3
2
Thus, the ratio k:1 is
3
2
:1, which simplifies to 2:3.