Question

If the y-axis divides the line joined by (2, 4) and (-3, 5),
then the ratio is
(a) 2:3
(c) 3:2
(b) 2:5
(d) 4:5​

Answer 1

Given :-

• y-axis divides a line joining points A(2,4) and B(-3,5).

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To find :-

• Ratio in which the line is divided by y-axis.

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Solution :-

• Let us consider the point P(0,y) at which the y-axis intersects the line.

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★ Using section formula

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$\to\bf\: \: \: {P(0,y) = \bigg( \dfrac{m_1x_2 + m_2x_1}{m_1 + m_2} , \dfrac{m_1y_2 + m_2y_1}{m_1 + m_2} \bigg)}$

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Now, let the ratio in which the line has been intersected be k : 1.

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$\: \: \: \therefore\bf\: \: \: {0 = \bigg( \dfrac{m_1x_2 + m_2x_1}{m_1 + m_2} \bigg)}$

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Here,

• $\sf{x_1 = 2\: , \: x_2 = -3}$
• $\sf{m_1 = k\: , \: m_2 = 1}$

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Putting the values

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$\tt:\implies\: \: \: \: \: \: \: \: {\bigg( \dfrac{(k \times 2) + (1 \times -3)}{k + 1} \bigg) = 0}$

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$\tt:\implies\: \: \: \: \: \: \: \: {\bigg(\dfrac{2k - 3}{k + 1} \bigg) = 0}$

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$\tt:\implies\: \: \: \: \: \: \: \: {2k - 3 = 0}$

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$\tt:\implies\: \: \: \: \: \: \: \: {2k = 3}$

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$\tt:\implies\: \: \: \: \: \: \: \: {k = \dfrac{3}{2}}$

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Hence,

• The required ratio is 3:2. Therefore (c) 3:2 is the correct option.