By section formula the coordinate of b is (3.8, 6.8).
According to the given question.
The endpoints of the line segment are a(3, 4) and c(5, 11).
Also, this line segment is partitioned by a point b such that ab and bc form a 2:3 ratio.
Le the coordinates of point b be (x, y).
From the section formula is used to find the coordinates of the point that divides a line segment in a ratio, either internally or externally.
Let M(x,y) be a point, dividing the line XY, with coordinates X (a, b) and Y (c, d), in a ratio m:n, internally.
Then, X = an + cm/(m + n) and Y = bn + dm/ (m + n)
Therefore, by section formula the coordinates of b is given by
x = 3(3) + 5(2)/(2 + 3)
⇒ x = 9 + 10/ 5
⇒ x = 19/5= 3.8
And,
y = 4(3) + 11(2)/(5)
⇒ y = 12 + 22/5
⇒ y = 34/5
⇒ y = 6.8
Hence, by section formula the coordinate of b is (3.8, 6.8).
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