Question

Q is the midpoint of line segment PM. Find midpoint Q.
Answers are Q is located at (11,1) (1,6) (1,0) (-1,0).

Answer 1

I'll try, the line from P to M is a red line that is vertical, P is at y, 2 and M is at y, -2

Answer 2

It looks like the only number for x is 1 because the red line going through P and M is only running through the one number and it's number 1. But the black horizontal line is going through the number 0

Answer 3

To find the midpoint \( Q \) of a line segment defined by two points \( P \) and \( M \), you would use the midpoint formula:

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

where \( (x_1, y_1) \) are the coordinates of point \( P \) and \( (x_2, y_2) \) are the coordinates of point \( M \).

Since the exact coordinates of points \( P \) and \( M \) are not provided in your question, we cannot calculate \( Q \) directly.

However, you provided potential answers for \( Q \):
- \( (11, 1) \)
- \( (1, 6) \)
- \( (1, 0) \)
- \( (-1, 0) \)

To determine which of these points could logically be a midpoint, you would need the coordinates of \( P \) and \( M \).

If you have any specific coordinates for \( P \) and \( M \), please provide them, and I can help calculate the midpoint \( Q \) for you. Otherwise, with the given information, we cannot determine which of the answer choices is correct.

Answer 4

Given that point \( P \) has coordinates \( (x, 2) \) and point \( M \) has coordinates \( (x, -2) \) (since the line is vertical, both points share the same \( x \)-coordinate), we can plug these values into the midpoint formula.

The midpoint \( Q \) is calculated as follows:

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

Substituting the coordinates of points \( P \) and \( M \):

- \( x_1 = x \), \( y_1 = 2 \)
- \( x_2 = x \), \( y_2 = -2 \)

Now, calculate:

\[
Q_x = \frac{x + x}{2} = \frac{2x}{2} = x
\]

\[
Q_y = \frac{2 + (-2)}{2} = \frac{0}{2} = 0
\]

So the midpoint \( Q \) has coordinates:

\[
Q = (x, 0)
\]

This means the \( y \)-coordinate of \( Q \) is \( 0 \) regardless of the value of \( x \).

From the possible answers you provided:
- \( (11, 1) \)
- \( (1, 6) \)
- \( (1, 0) \)
- \( (-1, 0) \)

The points \( (1, 0) \) and \( (-1, 0) \) have a \( y \)-coordinate of \( 0 \), while \( Q \) can have any \( x \)-coordinate. Therefore, either \( (1, 0) \) or \( (-1, 0) \) could correspond to the midpoint \( Q \).

If you would like more specific identification, please specify \( x \) for \( P \) and \( M \).

Answer 5

Given your clarification, if point \( P \) is at \( (1, 2) \) and point \( M \) is at \( (1, -2) \), we can find the midpoint \( Q \) again using the coordinates:

- \( P = (1, 2) \)
- \( M = (1, -2) \)

Using the midpoint formula:

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

Substituting the coordinates of points \( P \) and \( M \):

\[
Q_x = \frac{1 + 1}{2} = \frac{2}{2} = 1
\]

\[
Q_y = \frac{2 + (-2)}{2} = \frac{0}{2} = 0
\]

Thus, the coordinates of the midpoint \( Q \) are:

\[
Q = (1, 0)
\]

So the correct answer from your provided options is **\( (1, 0) \)**.