What are the coordinates of the point dividing the line segment intern

1.	What are the coordinates of the point dividing the line segment internally in the ratio of 3 : 1, end points of the line segments are (–2, 2) and (10,–6) ?1. (1,0)2. (4,-2)3. (7,-4)4. \((\frac{9}{2},3)\)
Answer» Correct Answer - Option 3 : (7,-4) Given: End points of the line segment are (–2, 2) and (10,–6) Ratio = 3 : 1 Formula Used: If end points of a line segment are (x₁, y₁) and (x_2, y₂) and point (x, y) divides the line segment internally in the ratio m : n \(x = \;\frac{{m{x_2} + n{x_1}}}{{m + n}}\;\;\;\;\;\;\;\;y = \;\frac{{m{y_2} + \;n{y_1}}}{{m + n}}\;\) Calculation: Let the coordinates of the point be (x, y) which divides the line segment in the ratio 3 : 1 \(x = \;\frac{{3 \times 10 + \;1 \times \left( { - 2} \right)}}{{3\; + \;1}}\;\;\) \( ⇒ x = \;\frac{{30\; - \;2}}{4}\;\;\) \(⇒ x = \;\frac{{28}}{4}\;\;\) ⇒ x = 7 \(\;y = \;\frac{{3 \times \left( { - 6} \right)\; + \;1 \times 2}}{{3\; + \;1}}\;\) \(\; ⇒ y = \;\frac{{ - 18 + \;2}}{4}\;\) \(\; ⇒ y = \;\frac{{ - 16}}{4}\;\) ⇒ y = –4 ∴ The coordinates of the point are (7, –4)

What are the coordinates of the point dividing the line segment internally in the ratio of 3 : 1, end points of the line segments are (–2, 2) and (10,–6) ?1. (1,0)2. (4,-2)3. (7,-4)4. \((\frac{9}{2},3)\)

Answer» Correct Answer - Option 3 : (7,-4)

Given:

End points of the line segment are (–2, 2) and (10,–6)

Ratio = 3 : 1

Formula Used:

If end points of a line segment are (x₁, y₁) and (x_2, y₂) and point (x, y) divides the line segment internally in the ratio m : n

\(x = \;\frac{{m{x_2} + n{x_1}}}{{m + n}}\;\;\;\;\;\;\;\;y = \;\frac{{m{y_2} + \;n{y_1}}}{{m + n}}\;\)

Calculation:

Let the coordinates of the point be (x, y) which divides the line segment in the ratio 3 : 1

\(x = \;\frac{{3 \times 10 + \;1 \times \left( { - 2} \right)}}{{3\; + \;1}}\;\;\)

\( ⇒ x = \;\frac{{30\; - \;2}}{4}\;\;\)

\(⇒ x = \;\frac{{28}}{4}\;\;\)

⇒ x = 7

\(\;y = \;\frac{{3 \times \left( { - 6} \right)\; + \;1 \times 2}}{{3\; + \;1}}\;\)

\(\; ⇒ y = \;\frac{{ - 18 + \;2}}{4}\;\)

\(\; ⇒ y = \;\frac{{ - 16}}{4}\;\)

⇒ y = –4

∴ The coordinates of the point are (7, –4)