Question
Given A(−1,2)
and B(3,6)
, find the coordinates of point X
on AB¯¯¯¯¯¯¯¯
such that the ratio of AX
to XB
is 3:5.(1 point)
Responses
(12,312)
Start Fraction 2 over 3 End Fraction
(125,425)
Start Fraction 1 over 3 End Fraction
(−14,312)
Start Fraction 3 over 2 End Fraction
(112,112)
and B(3,6)
, find the coordinates of point X
on AB¯¯¯¯¯¯¯¯
such that the ratio of AX
to XB
is 3:5.(1 point)
Responses
(12,312)
Start Fraction 2 over 3 End Fraction
(125,425)
Start Fraction 1 over 3 End Fraction
(−14,312)
Start Fraction 3 over 2 End Fraction
(112,112)
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To find point \( X \) on segment \( \overline{AB} \) that divides \( AB \) in the ratio \( 3:5 \), we can use the section formula. The coordinates of points \( A \) and \( B \) are given as:
- \( A(-1, 2) \)
- \( B(3, 6) \)
If the coordinates of point \( X \) that divides \( \overline{AB} \) in the ratio \( m:n \) are given as:
\[
X \left( \frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n} \right)
\]
where \( m = 3 \) and \( n = 5 \), and \( (x_1, y_1) = (-1, 2) \) and \( (x_2, y_2) = (3, 6) \).
Substituting these values into the formula:
1. For the x-coordinate of \( X \):
\[
x = \frac{3 \cdot 3 + 5 \cdot (-1)}{3 + 5} = \frac{9 - 5}{8} = \frac{4}{8} = \frac{1}{2}
\]
2. For the y-coordinate of \( X \):
\[
y = \frac{3 \cdot 6 + 5 \cdot 2}{3 + 5} = \frac{18 + 10}{8} = \frac{28}{8} = \frac{7}{2}
\]
Thus, the coordinates of point \( X \) are:
\[
X\left( \frac{1}{2}, \frac{7}{2} \right)
\]
Looking at the responses provided:
- \( (12,312) \)
- \( (125,425) \)
- \( (−14,312) \)
- \( (112,112) \)
None of the options provided match \( X\left( \frac{1}{2}, \frac{7}{2} \right) \).
Therefore, the calculation confirms the coordinates of \( X \) but does not align with any of the response options listed. If you need the result to be in a specific format or any clarification, please let me know!
- \( A(-1, 2) \)
- \( B(3, 6) \)
If the coordinates of point \( X \) that divides \( \overline{AB} \) in the ratio \( m:n \) are given as:
\[
X \left( \frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n} \right)
\]
where \( m = 3 \) and \( n = 5 \), and \( (x_1, y_1) = (-1, 2) \) and \( (x_2, y_2) = (3, 6) \).
Substituting these values into the formula:
1. For the x-coordinate of \( X \):
\[
x = \frac{3 \cdot 3 + 5 \cdot (-1)}{3 + 5} = \frac{9 - 5}{8} = \frac{4}{8} = \frac{1}{2}
\]
2. For the y-coordinate of \( X \):
\[
y = \frac{3 \cdot 6 + 5 \cdot 2}{3 + 5} = \frac{18 + 10}{8} = \frac{28}{8} = \frac{7}{2}
\]
Thus, the coordinates of point \( X \) are:
\[
X\left( \frac{1}{2}, \frac{7}{2} \right)
\]
Looking at the responses provided:
- \( (12,312) \)
- \( (125,425) \)
- \( (−14,312) \)
- \( (112,112) \)
None of the options provided match \( X\left( \frac{1}{2}, \frac{7}{2} \right) \).
Therefore, the calculation confirms the coordinates of \( X \) but does not align with any of the response options listed. If you need the result to be in a specific format or any clarification, please let me know!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.