Your Turn: Given points (0, 0) and (3, 6), find the point which partitions the segment into 3:2.
A. (1.8, 3.6)
B. (2,4)
C. (3,5)
D. (4.5, 9)
can you please help me
is it C
you want the point 3/5 of the way between, so (0,0) + (3/5)(3,6) = (9/5,18/5)
Looks like A.
Of course! To find the point which partitions the segment into a 3:2 ratio, we need to divide the total length of the segment into 5 equal parts (3 parts for the first segment and 2 parts for the second segment).
First, let's calculate the length of the entire segment. Using the distance formula, we find that the distance between the points (0, 0) and (3, 6) is:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
= sqrt((3 - 0)^2 + (6 - 0)^2)
= sqrt(9 + 36)
= sqrt(45)
= 3√5
So, the length of the segment is 3√5.
To find the point that partitions the segment into a 3:2 ratio, we need to calculate the distance from one end of the segment (0, 0) to the partition point. Let's call this distance d1.
d1 = (3/5) * length of segment
= (3/5) * 3√5
= (9/5)√5
≈ 4.0488
Now, we know that the x-coordinate of the partition point is given by the ratio 3:2. Therefore, we can calculate the x-coordinate by multiplying the total x-distance (3) with the ratio (2/5):
x-coordinate = (2/5) * 3
= 6/5
= 1.2
Similarly, we can calculate the y-coordinate by multiplying the total y-distance (6) with the ratio (2/5):
y-coordinate = (2/5) * 6
= 12/5
= 2.4
Therefore, the partition point is approximately (1.2, 2.4).
Comparing this with the given options, we can see that the closest option to (1.2, 2.4) is option A. (1.8, 3.6).
So, the correct answer is A. (1.8, 3.6).