Question

PLEASEEEEE HELPPPPPPP!!!!!!!

A line segment contains endpoints A(-1, 2) and B(2, 5).
Determine the point that partitions line segment AB into a 3: 6 ratio.

A 4,5/3
B 0,3
C 1/3,3
D -2,1

Answer 1

We can find the point that partitions line segment AB into a 3:6 ratio by using the formula for finding a point that divides a line segment into two parts in a given ratio.

Let's call the point we're looking for "P". According to the formula, the coordinates of point P can be found using the following equations:

x-coordinate of P = [(6 * x-coordinate of A) + (3 * x-coordinate of B)] / 9

y-coordinate of P = [(6 * y-coordinate of A) + (3 * y-coordinate of B)] / 9

Using the coordinates of points A and B given in the problem, we can plug them into these equations and simplify to find the coordinates of point P:

x-coordinate of P = [(6 * -1) + (3 * 2)] / 9 = 0

y-coordinate of P = [(6 * 2) + (3 * 5)] / 9 = 3.33 (rounded to two decimal places)

Therefore, the point that partitions line segment AB into a 3:6 ratio is approximately (0, 3.33), which is closest to option A: 4,5/3.