Question

The points which divides the line segment of points P(-1, 7) and Q(4, -3) in the ratio of 2:3 is______.
(a)(-1, 3)
(b)(-1, -3)
(c)(1, 3)
(d)(1, -3)

Answer 1

Answer:

1,3 option no c is the correct one

Step-by-step explanation:

take ratio as m

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Answer 2

Answer:

Option C : (1, 3)

Step-by-step explanation:

Given:

• Point P (-1, 7)
• Point Q (4, -3)
• Ratio = 2 : 3

To Find:

• The coordinates of the point which divides the line

Solution:

Here we have to find the point which divides the line segment in the ratio   2 : 3

By section formula we know that,

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

Where m₁ = 2, m₂ = 3, x₁ = -1, x₂ = 4, y₁ = 7, y₂ = -3

Substitute the data,

$\tt{(x,y)=\bigg(\dfrac{8-3}{2+3},\dfrac{-6+21}{2+3}\bigg)}$

$\tt{(x,y)=\bigg(\dfrac{5}{5},\dfrac{15}{5}\bigg)}$

Equating the x coordinate

x = 5/5

x = 1

Hence the x coordinate of the point is 1.

Equate the y coordinate,

y = 15/5

y = 3

Hence the y coordinate of the point is 3.

Hence the point which divides the line segment is (1, 3)

Therefore option c is correct.

Notes:

The section formula is given by,

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