Find the coordinates of the points which divides the line segment joining the point( (-2,0)and(0,8) in 4 equal parts
Answers
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Given:
The line segment of points A(-2, 0) and B(0, 8).
To Find:
The coordinates of the points divide the line segment into four equal parts.
Solution:
Let us consider P, Q and R are the points that divide the line segment into four equal parts.
A(-2, 0) and B(0, 8) where,
x₁ = -2, x₂ = 0, y₁ = 0, y₂ =8
For point P which divides line segment AB internally with a ratio of 1:3
where m =1 and n = 3.
Using the section formula, we know
P(x, y) = [(mx₂ + nx₁) / m+n, (my₂ + ny₁) / m+n]
= [(1×0 +3×(-2)) / 1+3, (1×8 + 3×0) / 1+3]
= (-6/4, 8/4])
= (-3/2, 2)
For point Q which divides line segment AB internally with a ratio of 1:1
where m =1 and n = 1
Using the section formula, we know
Q(x, y) = [(mx₂ + nx₁) / m+n, (my₂ + ny₁) / m+n]
= [(1×0 +1×(-2)) / 1+1, (1×8 + 1×0) / 1+1]
= (-2/2, 8/2)
= (-1, 4)
For point R which divides line segment AB internally with a ratio of 3:1
where m =3 and n = 1
Using the section formula, we know
R(x, y) = [(mx₂ + nx₁) / m+n, (my₂ + ny₁) / m+n]
= [(3×0 +1×(-2)) / 3+1, (3×8 + 1×0) / 3+1]
= (-2/4, 24/4)
= (-1/2, 6)
Therefore, The coordinates of the point which divides the line segment into four equal parts are (-3/2, 2), (-1,4), and (-1/2,6).
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