A(2, 4) and B(8, 12) are two ends of a line segment. Find the point which divides AB internally in the ratio 1:3
Question
A(2, 4) and B(8, 12) are two ends of a line segment.
Find the point which divides AB internally in the ratio 1:3.
Solution
To find the point that divides the line segment AB in the ratio 1:3, we can use the formula for section formula in coordinate geometry. The formula is:
((m1x2 + m2x1) / (m1 + m2), (m1y2 + m2y1) / (m1 + m2))
where (x1, y1) and (x2, y2) are the coordinates of points A and B respectively, and m1:m2 is the given ratio.
Here, A(2, 4) and B(8, 12) are the coordinates of points A and B. So, x1 = 2, y1 = 4, x2 = 8, y2 = 12. The given ratio is 1:3, so m1 = 1, m2 = 3.
Substituting these values into the formula, we get:
((18 + 32) / (1 + 3), (112 + 34) / (1 + 3))
Solving this, we get:
((8 + 6) / 4, (12 + 12) / 4)
So, the point that divides the line segment AB in the ratio 1:3 is (3.5, 6).
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