Question : In what ratio does the point T(3,0) divide the segment joining the points S(4,–2) and U(1, 4)?
Option 1: $2:1$
Option 2: $1:2$
Option 3: $2:3$
Option 4: $3:2$
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Correct Answer: $1:2$
Solution :
Given: The point T(3,0) divide the segment joining the points S(4,-2) and U(1,4)
Let point T divide line segment SU in the ratio k:1.
If the coordinates of point T be ($x$, $y$) and that of points S and U be $(x_1, y_1)$ and $(x_2, y_2)$ respectively, then
$x = \frac{kx_2+x_1}{k+1}$; $y = \frac{ky_2+y_1}{k+1}$
$\therefore 3 = \frac{k×1+1×4}{k+1}$
⇒ $3k+3 = k+4$
⇒ $2k = 1$
⇒ $k = \frac{1}{2}$ = $1:2$
Hence, the correct answer is $1:2$
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