Line segment AB has endpoints A(10, 4) and B(2, 8). Find the coordinates of the point that divides the line segment directed from A to B in the ratio of 1:4.
A) (6, 6)
B) (2, 56/5)
C) (24/5, 42/5)
D) (42/5, 24/5)***
Your are correct.
D.) (42/5, 24,5) is the right answer.
To find the coordinates of the point that divides the line segment directed from A to B in the ratio of 1:4, you can use the section formula.
The section formula states that if a line segment AB is divided by a point P in the ratio of m:n, then the coordinates of point P can be found using the following formula:
Px = (n * Ax + m * Bx) / (m + n)
Py = (n * Ay + m * By) / (m + n)
where (Ax, Ay) and (Bx, By) are the coordinates of points A and B, respectively, and (Px, Py) are the coordinates of the point that divides the line segment.
Given that A(10, 4) and B(2, 8), and the ratio is 1:4 (m:n = 1:4), we can substitute the values into the formula to find the coordinates of the point.
Px = (4 * 2 + 1 * 10) / (1 + 4) = (8 + 10) / 5 = 18 / 5 = 3.6
Py = (4 * 8 + 1 * 4) / (1 + 4) = (32 + 4) / 5 = 36 / 5 = 7.2
Therefore, the coordinates of the point that divides the line segment AB in the ratio of 1:4 are approximately (3.6, 7.2).
Among the given answer choices, the closest option is D) (42/5, 24/5), so the correct answer is D).