Question

What's the answer? Also please tell the steps of the solution.
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Answer 1

`\rm\displaystyle D) \left (1,3\right)`

Explanation:

well to figure out the point we can consider the following formula:

`\rm\displaystyle \text C(x,y)= \left ((m x_(2) + n x_(1) )/(m + n) , (m y_(2) + n y_(1) )/(m + n) \right)`

from the given we acquire that,

• 
  `(x _(1), y_(1)) = ( - 1,7)`
• 
  `(x _(2), y_(2)) = ( 4, - 3)`
• 
  `m : n = 2 : 3`

therefore substitute:

`\rm\displaystyle \text C(x,y)= \left (((2) (4)+ 3( - 1) )/(2 + 3) , ((2) ( - 3) + (3)(7))/(2 + 3) \right)`

simplify multiplication:

`\rm\displaystyle \text C(x,y)= \left ((8 - 3 )/(2 + 3) , ( - 6+ 21)/(2 + 3) \right)`

simplify:

`\rm\displaystyle \text C(x,y)= \left ((5)/(5) , ( 15)/(5) \right)`

simplify division:

`\rm\displaystyle \text C(x,y)= \left (1,3\right)`

hence our answer is D)

Answer 2

`\huge\boxed{\mathfrak{Answer}}`

Points => (-1, 7) & (4, -3)

Ratio => 2 : 3

(x₁, y₁) = (-1, 7)

(x₂, y₂) = (4, -3)

(m₁, m₂) = (2, 3)

Formula =
`\large\left ((m_(1) x_(2) + m_(2) x_(1) )/(m_(1) + m_(2)) , (m_(1) y_(2) + m_(2) y_(1) )/(m_(1) + m_(2)) \right)`

Points which divide the line segment

=
`( (2 * 4 + 3 * - 1)/(2 + 3), (2 * -3 + 3 * 7)/(2 + 3))`

`=( (8 - 3)/(5) , ( - 6 + 21)/(5)) \\ = ( (5)/(5) , (15)/(5) ) \\ = (1,3)`

Answer => (1, 3) [option D]