The coordinates of point B are (12, 12).
Given,
Point C(6,9) is located on the segment between point A(4,8) and point B. The ratio of AC to CB is 1:3.
We need to find the coordinates of point B.
What is the coordinates of a point P that divides two points A and B in the ratio m:n?
If the two points A and B have coordinates (x_1,y_1) and (x_2, y_2)
The coordinates of P are given by :
x = (mx_2 + nx_1) / m+n
y = (my_2 + ny_1) / m+n
We have,
C(6,9) = C(x, y) is the midpoint of A(4,8) = (x_1, y_1) and B(x_2, y_2) and
m:n = 1:3.
We have,
x = (mx_2 + nx_1) / m+n
6 = (1 x x_2 + 3 x 4) / 1 + 3
6 = (x_2 + 12) / 4
6 x 4 = x_2 + 12
24 = x_2 + 12
24 - 12 = x_2
x_2 = 12
y = (my_2 + ny_1) / m+n
9 = (1 x y_2 + 3 x 8) / 4
9 = (y_2 + 24) / 4
36 = y_2 + 24
36 - 24 = y_2
y_2 = 12
Find the coordinates of point B
Point B has coordinates as (x_2, y_2).
(x_2, y_2) = ( 12, 12 )
Thus the coordinates of point B are (12, 12).
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