Question

The point which divides the line segment joining the points A (0, 5) and
B (5, 0) internally in the ratio 2:3 is _____________

Answer 1

Answer: (2,3)

Step-by-step explanation:

Given: $A(x_1,y_1) = (0,5)$

            $A(x_2,y_2) = (5,0)$ and ratio $m_1:m_2= 2:3$ divides internally

As we know by section formula

$(x,y) = (\dfrac{m_1x_2+m_2x_1}{m_1+m_2}, \dfrac{m_1y_2+m_2y_1}{m_1+m_2})$

Therefore

$(x,y) = (\dfrac{2\times 5+ 3\times 0}{2+3}, {\dfrac{2\times 0+ 3 \times 5}{2+3}) = (2,3)$

Hence, the coordinate is (2,3)

Answer 2

Answer:

$\red { Required \:point } \green { = ( 2,3 ) }$

Step-by-step explanation:

$Given \: two \: points \: A(0,5) = (x_{1},y_{1}) \\and \: B(5,0) = (x_{2},y_{2})$

$Let \: the \:point \:P(x,y) \:divides \: the \:line \\AB \:in \:the \:ratio \: m:n = 2:3$

$\underline { \pink { By \:Section \: Formula:}}$

$\boxed {\orange { P = \left( \frac{mx_{2}+nx_{1}}{m+n} , \frac{my_{2}+ny_{1}}{m+n} \right)}}$

$P = \left( \frac{2\times 5+3\times 0}{3+2},\frac{2\times 0+3\times 5}{3+2}\right)\\= \left( \frac{10}{5} , \frac{15}{5}\right)\\= ( 2 , 3 )$

Therefore.,

$\red { Required \:point } \green { = ( 2,3 ) }$

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