Question : Point A divides segment BC in the ratio 4 : 1. Coordinates of B are (6, 1) and coordinates of C are ( $\frac{7}{2}$ , $6$ ). What are the coordinates of point A?
Option 1: (4, 3)
Option 2: (4, 5)
Option 3: (2, 5)
Option 4: (3, 5)

Question

Question : If $\frac{(a + b)}{c} = \frac{6}{5}$ and $\frac{(b + c)}{a} = \frac{9}{2}$ , then what is the value of $\frac{(a + c)}{b} ?$
Option 1: $\frac{9}{5}$
Option 2: $\frac{11}{7}$
Option 3: $\frac{7}{11}$
Option 4: $\frac{7}{4}$

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Answer 1

Correct Answer: (4, 5)

Solution : The point A coordinates by using 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 $m : n$ .
Given: $m = 4$ , $n = 1$ , $x_{1} = 6, y_{1} = 1, x_{2} = \frac{7}{2}, and y_{2} = 6$
From the section formula, the $x$ coordinate of A $= \frac{4 \times \frac{7}{2} + 1 \times 6}{4 + 1}$
$= \frac{20}{5} = 4$
Similarly, the y coordinate of A is $\frac{4 \times 6 + 1 \times 1}{4 + 1}$ .
$= \frac{25}{5} = 5$
The coordinates of point A are (4, 5).
Hence, the correct answer is (4, 5).

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Question : Point A divides segment BC in the ratio 4 : 1. Coordinates of B are (6, 1) and coordinates of C are (72, 6). What are the coordinates of point A?Option 1: (4, 3)Option 2: (4, 5)Option 3: (2, 5)Option 4: (3, 5)

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Question : Point A divides segment BC in the ratio 4 : 1. Coordinates of B are (6, 1) and coordinates of C are ( $\frac{7}{2}$ , $6$ ). What are the coordinates of point A?
Option 1: (4, 3)
Option 2: (4, 5)
Option 3: (2, 5)
Option 4: (3, 5)