Question
A segment goes from (2,5) to (10,5) where should a point be placed on the segment to split it into a ratio 1:3
between the left and right parts.
8
-6-
-2-
0
2
4
6
8
10
12
between the left and right parts.
8
-6-
-2-
0
2
4
6
8
10
12
Answers
GPT-4o mini
To split the segment from (2, 5) to (10, 5) into a ratio of 1:3, we first need to determine the total length of the segment and then find the coordinates of the point that divides it in the desired ratio.
The segment runs horizontally along the line \( y = 5 \) from \( x = 2 \) to \( x = 10 \). The length of the segment is:
\[
10 - 2 = 8
\]
To split this segment in the ratio \( 1:3 \), we will calculate the length of each part. The total parts in the ratio \( 1 + 3 = 4 \).
- Length of the left part (1 part): \( \frac{1}{4} \) of the total length = \( \frac{1}{4} \times 8 = 2 \)
- Length of the right part (3 parts): \( \frac{3}{4} \) of the total length = \( \frac{3}{4} \times 8 = 6 \)
Starting from the left endpoint (2, 5), we will move rightwards by the length of the left part:
\[
x = 2 + 2 = 4
\]
The y-coordinate remains the same since it is a horizontal segment (y = 5).
Thus, the point that splits the segment into a ratio of 1:3 is:
\[
\text{Point} = (4, 5)
\]
This point divides the segment from (2, 5) to (10, 5) into two parts, one with length 2 (from (2, 5) to (4, 5)) and the other with length 6 (from (4, 5) to (10, 5)).
The segment runs horizontally along the line \( y = 5 \) from \( x = 2 \) to \( x = 10 \). The length of the segment is:
\[
10 - 2 = 8
\]
To split this segment in the ratio \( 1:3 \), we will calculate the length of each part. The total parts in the ratio \( 1 + 3 = 4 \).
- Length of the left part (1 part): \( \frac{1}{4} \) of the total length = \( \frac{1}{4} \times 8 = 2 \)
- Length of the right part (3 parts): \( \frac{3}{4} \) of the total length = \( \frac{3}{4} \times 8 = 6 \)
Starting from the left endpoint (2, 5), we will move rightwards by the length of the left part:
\[
x = 2 + 2 = 4
\]
The y-coordinate remains the same since it is a horizontal segment (y = 5).
Thus, the point that splits the segment into a ratio of 1:3 is:
\[
\text{Point} = (4, 5)
\]
This point divides the segment from (2, 5) to (10, 5) into two parts, one with length 2 (from (2, 5) to (4, 5)) and the other with length 6 (from (4, 5) to (10, 5)).