Question

Determine the coordinates of point J
on AB¯¯¯¯¯¯¯¯
so that the ratio of AJ
to JB
is 1:1.

(1 point)
Responses

J(0,2)
upper J left parenthesis 0 comma 2 right parenthesis

J(3,0)
upper J left parenthesis 3 comma 0 right parenthesis

J(0,−3)
upper J left parenthesis 0 comma negative 3 right parenthesis

J(0,3)
upper J left parenthesis 0 comma 3 right parenthesis

Answer 1

To find the coordinates of point \( J \) on line segment \( AB \) such that the ratio \( AJ : JB = 1 : 1 \), point \( J \) must be the midpoint of segment \( AB \).

1. First, identify the coordinates of points \( A \) and \( B \). However, they are not provided in the question. We would typically denote them as \( A(x_1, y_1) \) and \( B(x_2, y_2) \).

2. The midpoint \( J \) of the line segment connecting points \( A \) and \( B \) can be calculated using the midpoint formula:
\[
J\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)
\]

Since you provided specific coordinate options for \( J \), I will check the provided coordinates against whatever \( A \) and \( B \) represent, keeping in mind that to maintain a ratio of \( 1:1 \), \( J \) must be at the midpoint.

- \( J(0,2) \)
- \( J(3,0) \)
- \( J(0,-3) \)
- \( J(0,3) \)

Without the coordinates of points \( A \) and \( B \), it's impossible to precisely identify which of these options correctly represents \( J \). However, if we assume \( A \) and \( B \) happen to be such that \( (0,2) \) or any other options are valid midpoints, we could assess each.

To conclude, if you have specific coordinates for point \( A \) and point \( B \), please provide them to determine which option correctly represents point \( J \) as the midpoint of \( AB \).