Question 10 of 18beginner🔧 ApplyNumerical2 marks

Find the coordinates of the point which divides the join of (-1, 7) and (4, -3) in the ratio 2:3.

Correct Answer

(1, 3)

Exercise: EXERCISE 7.2 | Q: 1 | (Page 13)
For More Understanding

Explanation

This question is solved using the section formula demonstrated in Example 6 of the provided text. The formula calculates the coordinates of a point dividing a line segment internally in a given ratio.

Solution Steps

  1. Let the given points be (−1,7)(-1, 7) and (4,−3)(4, -3), and let the ratio be m1:m2=2:3m_1 : m_2 = 2:3.

  2. Using the section formula as shown in Example 6:

    x=m1x2+m2x1m1+m2,y=m1y2+m2y1m1+m2x = \frac{m_1 x_2 + m_2 x_1}{m_1 + m_2}, \quad y = \frac{m_1 y_2 + m_2 y_1}{m_1 + m_2}

  3. Calculating x-coordinate:

    x=2(4)+3(−1)2+3=8−35=55=1x = \frac{2(4) + 3(-1)}{2 + 3} = \frac{8 - 3}{5} = \frac{5}{5} = 1

  4. Calculating y-coordinate:

    y=2(−3)+3(7)2+3=−6+215=155=3y = \frac{2(-3) + 3(7)}{2 + 3} = \frac{-6 + 21}{5} = \frac{15}{5} = 3

  5. Therefore, the coordinates of the required point are (1, 3).

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