Question : In what ratio does the point T (X, 0) divide the segment joining the points S (–4, –1) and U (1, 4)?
Option 1: 1 : 4
Option 2: 4 : 1
Option 3: 1 : 2
Option 4: 2 : 1
Correct Answer: 1 : 4
Solution :
Given:
Point T(X, 0) divides the line segment SU. The coordinates of S are (–4, –1) and U are (1, 4).
Let the point T(X,0) divide the line segment SU in the ratio $m : n$.
The section formula, $A(x,y)=(\frac{m\times x_2 + n\times x_1}{m+n},\frac{m\times y_2 + n \times y_1} {m+n})$ where $A(x_1,y_1)$ and $B(x_2,y_2)$ are the coordinates of the points which divides the line segment in the ratio $m:n$.
Here, the $y$ coordinate of T $=\frac{m\times y_2 + n \times y_1} {m+n}=0$
⇒ ($\frac{4\times m–n} {m+n})=0$.
⇒ $4m=n$
⇒ $\frac{m}{n}=1: 4$
The ratio is 1 : 4 in which the given point T(X, 0) divides the line segment SU.
Hence, the correct answer is 1 : 4.
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