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: $3 : 2$

Question

Question : The point P is the midpoint of the segment AB. The coordinates of point P are (2, 1) and that of point A are (11, 5). The coordinates of point B are:
Option 1: (–7, –3)
Option 2: (6.5, 3)
Option 3: (7, 3)
Option 4: (–6.5, –3)

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Answer 1

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
$x = \frac{k x_{2} + x_{1}}{k + 1}$ ; $y = \frac{k y_{2} + y_{1}}{k + 1}$
$∴ 3 = \frac{k \times 1 + 1 \times 4}{k + 1}$
⇒ $3 k + 3 = k + 4$
⇒ $2 k = 1$
⇒ $k = \frac{1}{2}$ = $1 : 2$
Hence, the correct answer is $1 : 2$

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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: 2:1Option 2: 1:2Option 3: 2:3Option 4: 3:2

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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: $3 : 2$