Use the image to answer the question.

Question

Segment upper A upper B is graphed on a coordinate plane. The x-axis ranges from negative 5 to 2 in increments of 1. The y-axis ranges from negative 4 to 3 in increments of 1.

Find the coordinates of point X if it partitions the directed segment AB¯¯¯¯¯¯¯¯ in the ratio 1:2 .

(1 point)
Responses

X(−213,−113)
upper X left parenthesis negative Start Fraction 7 over 3 End Fraction comma negative 2 right parenthesis

X(−1,−23)
upper X left parenthesis negative 1 comma negative Start Fraction 2 over 3 End Fraction right parenthesis

X(−5,−423)
upper X left parenthesis negative 5 comma negative Start Fraction 14 over 3 End Fraction right parenthesis

X(−514,−212)

Answer 1

To find the coordinates of point \( X \) that partitions segment \( \overline{AB} \) in the ratio \( 1:2 \), we can use the section formula. The formula for a point dividing a segment in the ratio \( m:n \) is given by:

\[ X = \left( \frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n} \right) \]

where \( (x_1, y_1) \) are the coordinates of point \( A \) and \( (x_2, y_2) \) are the coordinates of point \( B \), and \( m \) and \( n \) are the ratio parts.

Since the coordinates of points \( A \) and \( B \) are not provided, let's assume we have their coordinates. If you can provide the coordinates of points \( A \) and \( B \), I can calculate point \( X \). Alternatively, if you provide any option that you consider for \( X \), I can narrow down the choices for you.

Please provide the coordinates of points \( A \) and \( B \) if you have them, or any other relevant details that may help.