Use the image to answer the question.

A line segment on a coordinate plane. The x-axis ranges from negative 4 to 0 in unit increments. The y-axis ranges from negative 3 to 5 in unit increments. The line extends straight down from point upper A to point upper M.

If R
is the midpoint of segment AM¯¯¯¯¯¯¯¯¯
, find midpoint R
.

(1 point)
Responses

R
is located at (−2,7)
.
upper B is located at left parenthesis negative 2 comma 7 right parenthesis .

R
is located at (−2,2.5)
.
upper B is located at left parenthesis negative 2 comma 2.5 right parenthesis .

R
is located at (−2,−2)
.
upper B is located at left parenthesis negative 2 comma negative 2 right parenthesis .

R
is located at (0,2.5)
.
upper B is located at left parenthesis 0 comma 2.5 right parenthesis .
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1 answer

To find the midpoint \( R \) of the line segment \( AM \), you'll need the coordinates of points \( A \) and \( M \). Since we don’t have a visual of the image to identify these points, we can infer based on the options given.

The midpoint \( R \) of a segment with endpoints \( (x_1, y_1) \) and \( (x_2, y_2) \) is calculated using the formula:

\[ R = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]

Given the choices for the midpoint \( R \):

  1. \( R \) is at \( (-2, 7) \)
  2. \( R \) is at \( (-2, 2.5) \)
  3. \( R \) is at \( (-2, -2) \)
  4. \( R \) is at \( (0, 2.5) \)

If we assume that \( A \) and \( M \) are positioned on a vertical line (since it states that \( AM \) extends straight down), this implies they have the same x-coordinate.

Starting with the y-coordinates given in the options, if we consider reasonable bounds based on the coordinate plane mentioned, we should see how the y-coordinates average to yield the choices.

  • For \( R = (-2, 2.5) \):
    • If \( A \) was at \( (-2, 5) \) and \( M \) at \( (-2, 0) \), then: \[ R = \left( -2, \frac{5 + 0}{2} \right) = \left( -2, 2.5 \right) \]

None of the other options yield logical pairs when applying the midpoint formula based on typical coordinates that fit on the given axes.

Thus, based on the calculation, the correct choice is \( R \) is located at \( (-2, 2.5) \).