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If point Q is the midpoint of segment AM¯¯¯¯¯¯¯¯¯ , find midpoint Q . (1 point)

Q is located at (1.5,−0.5) . upper B is located at left parenthesis 1.5 comma negative 0.5 right parenthesis . Q is located at (−9,−8) . upper B is located at left parenthesis negative 9 comma negative 8 right parenthesis . Q is located at (−2.5,3.5) . upper B is located at left parenthesis negative 2.5 comma 3.5 right parenthesis . Q is located at (12,7) .

3 answers

To find the midpoint \( Q \) of segment \( \overline{AM} \), we can use the midpoint formula. The midpoint \( Q \) of a segment with endpoints \( A(x_1, y_1) \) and \( M(x_2, y_2) \) is given by:

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

From your question, it seems you are also identifying some coordinates for point \( Q \) (midpoints) and point \( B \) with coordinates given. However, it is unclear if these points are endpoints of segment \( AM \) or just isolated values.

If point \( Q \) is at (1.5, -0.5) and we are to consider that point as a valid midpoint (without any further information), then the segment has endpoints \( A \) and \( M \) that can be calculated provided we know one point among them.

If we assume one of the coordinates you provided is meant to represent endpoint \( A \) or \( M \):

  1. If \( A = (-9, -8) \), then we can set \( Q \) and solve for \( M \): \[ (1.5, -0.5) = \left(\frac{-9 + x_2}{2}, \frac{-8 + y_2}{2}\right) \] Solving these equations gives: \[ \frac{-9 + x_2}{2} = 1.5 \quad \Rightarrow \quad -9 + x_2 = 3 \quad \Rightarrow \quad x_2 = 12 \] \[ \frac{-8 + y_2}{2} = -0.5 \quad \Rightarrow \quad -8 + y_2 = -1 \quad \Rightarrow \quad y_2 = 7 \] Thus, point \( M \) is \( (12, 7) \), and \( Q \) lies correctly at \( (1.5, -0.5) \).

To summarize, if we confirm the coordinate for the segment \( AM \) that includes \( Q \), we find positions uniquely for \( A \) and \( M \) based on midpoint calculation. This can be repeated for other provided points \( (-2.5, 3.5) \) or any other given combinations.

If you meant for me to find the midpoint of other points listed, please clarify so we could explore other options properly.

so what is the midpoint of Q?

The term "midpoint of Q" can be a bit confusing because a midpoint typically references a segment defined by two endpoints. Given that point \( Q \) itself represents a specific point and does not have two distinct endpoints associated with it in your question, we cannot compute a midpoint for a single point.

However, if you are asking for the specific coordinate of point \( Q \) as defined in your original message, here are the midpoints provided:

  1. When \( Q = (1.5, -0.5) \), you mentioned this as location of midpoint Q.
  2. When \( Q = (-9, -8) \), then \( Q \) is again provided as the coordinates for another context.
  3. When \( Q = (-2.5, 3.5) \) also includes Q's coordinate.
  4. Finally, \( Q = (12, 7) \) stated.

If you're looking for the definition of the midpoint of two specific points (i.e. calculating a midpoint but providing new A and M), please provide further instructions, or if you need the overall value amid your listings.

These coordinates you provided are specifically locations of point \( Q \) and are not midpoints in relation to other points unless more clarity is given regarding segments for calculation purposes. Please clarify further if needed!