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)
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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)
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Answer:
1,3 option no c is the correct one
Step-by-step explanation:
take ratio as m
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Answer:
Option C : (1, 3)
Step-by-step explanation:
Given:
To Find:
Solution:
Here we have to find the point which divides the line segment in the ratio 2 : 3
By section formula we know that,
[tex]\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)}[/tex]
Where m₁ = 2, m₂ = 3, x₁ = -1, x₂ = 4, y₁ = 7, y₂ = -3
Substitute the data,
[tex]\tt{(x,y)=\bigg(\dfrac{8-3}{2+3},\dfrac{-6+21}{2+3}\bigg)}[/tex]
[tex]\tt{(x,y)=\bigg(\dfrac{5}{5},\dfrac{15}{5}\bigg)}[/tex]
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,
[tex]\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)}[/tex]