Question

The coordinates of the point which internally divides the line segment joint (3, -5) and (8, 5) in the ratio 2 : 3 are
a) (5,1)
b) (5,-1)
c) (-5,1)
d) (-5,-1)​

Answer 1

We will use section formula to solve this question.

Coordinates (x, y) of a point which divides two points on cartesian plane say (x1, y1) and (x2, y2) in the ratio m1 : m2 is given as-

$\underline{\boxed{ \sf(x,y) = \left( \frac{m_1x_2 + m_2x_1}{m_1 + m_2},\frac{m_1y_2 + m_2y_1}{m_1 + m_2} \right)}} \bigstar$

By the information provided in the question, let us assume that:

• m1 : m2 = 2 : 3
• (x1, y1) = (3, -5)
• (x2, y2) = (8, 5)

So, make use of above formula-

${: \implies \sf(x,y) = \left( \dfrac{m_1x_2 + m_2x_1}{m_1 + m_2},\dfrac{m_1y_2 + m_2y_1}{m_1 + m_2} \right)}$

${: \implies \sf(x,y) = \left( \dfrac{2(8)+ 3(3)}{2 + 3},\dfrac{2(5) + 3( - 5)}{2 + 3} \right)}$

${: \implies \sf(x,y) = \left( \dfrac{16+ 9}{5},\dfrac{10 - 15}{5} \right)}$

${: \implies \sf(x,y) = \left( \dfrac{25}{5},\dfrac{ - 5}{5} \right)}$

${: \implies \sf(x,y) = \left( 5, - 1 \right)}$

So, option (b) is correct.

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