Question

Use the image to answer the question.

Segment upper A upper B is graphed on a coordinate plane. The x-axis ranges from negative 2 to 2 in increments of 1. The y-axis ranges from negative 1 to 7 in increments of 1.

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

J(0,−3)

Answer 1

To find point J on segment AB such that the ratio of AJ to JB is 1:1, we need to find the midpoint of segment AB, as the midpoint divides the segment into two equal lengths.

Since the actual coordinates of points A and B are not provided, we need to choose one of the response options that could realistically be a midpoint.

Given that the options provided are:

1. J(0,2)
2. J(0,3)
3. J(0,−3)

The option that would be the most reasonable as a midpoint based on conventional graphical representations, without specific coordinates for A and B, is J(0,2) or J(0,3). However, we cannot definitively choose between them without being able to identify points A and B.

If we assume segment AB is on the y-axis as indicated by the x-coordinate of J being 0, and since we know no further details, I would select:

**Response: J(0,2)**

This point is often closer to the mid-range in scenarios where A and B could have been chosen from that portion of the graph. However, remember that without exact coordinates for A and B, this is an assumption.