MCQ
The point $P$ which divides the line segment joining the points $A(2, -5)$ and $B(5, 2)$ in the ratio $2 : 3$ lies in the quadrant.
- A$I$
- B$II$
- C$III$
- ✓$IV$
✓
Answer
Correct option: D.
$IV$
P divides AB in the ratio $2 : 3$.
Let the coordinates of $P$ be $(x, y)$.
We know that, the centra is the mid-point of the diameter.
Using the section formula, we get:
$(\text{x},\text{y})=\Big(\frac{2(5)+3(2)}{2+3},\frac{2(2)+3(-5)}{2+3}\Big)$
$\Rightarrow\ (\text{x},\text{y})=\Big(\frac{16}{5},\frac{-11}{5}\Big)$
We know that, points of the from $(a, -b)$ lie in quadrant IV.
Let the coordinates of $P$ be $(x, y)$.
We know that, the centra is the mid-point of the diameter.
Using the section formula, we get:
$(\text{x},\text{y})=\Big(\frac{2(5)+3(2)}{2+3},\frac{2(2)+3(-5)}{2+3}\Big)$
$\Rightarrow\ (\text{x},\text{y})=\Big(\frac{16}{5},\frac{-11}{5}\Big)$
We know that, points of the from $(a, -b)$ lie in quadrant IV.
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