To find the midpoint \( R \) of line segment \( AM \), we need the coordinates of points \( A \) and \( M \). Since the question describes a vertical line segment (extending straight down), we can assume that both points share the same x-coordinate.
Let’s denote the coordinates of point \( A \) as \( (x_A, y_A) \) and point \( M \) as \( (x_M, y_M) \). The midpoint \( R \) can be calculated using the midpoint formula:
\[ R = \left(\frac{x_A + x_M}{2}, \frac{y_A + y_M}{2}\right) \]
Given that the segment is vertical, \( x_A = x_M \), which means \( x_R = x_A \). Therefore, the x-coordinate of midpoint \( R \) is simply the x-coordinate of points \( A \) and \( M \).
We can find the midpoint \( y_R \) by averaging the y-coordinates of \( A \) and \( M \):
\[ y_R = \frac{y_A + y_M}{2} \]
Without specific coordinates provided for \( A \) and \( M \) from the image, we can't compute the exact location of midpoint \( R \). However, let’s consider the possible answers given.
Since we know that the line segment extends vertically, we should expect the x-coordinates of options to match that of point \( A \) or \( M \), while the average y-coordinate should determine the y-value for \( R \).
- Option 1: \( R \) is located at \( (-2, -2) \)
- Option 2: \( R \) is located at \( (0, 2.5) \)
- Option 3: \( R \) is located at \( (-2, 2.5) \)
- Option 4: \( R \) is located at \( (-2, 7) \)
We look for consistency between the options and our understanding of a vertical segment. If \( A \) has a y-coordinate higher than \( M \), then \( R \)'s y-value should logically fall between the two.
However, without the specific coordinates, we cannot determine which option is correct.
If given the y-coordinates of \( A \) and \( M \) as \( -2 \) and \( 7 \) respectively, for example:
- \( A(-2, 7) \)
- \( M(-2, -2) \)
The midpoint calculation would yield: \[ R = \left(-2, \frac{7 + (-2)}{2}\right) = (-2, 2.5) \] This would suggest that option 3, \( R \) is located at \( (-2, 2.5) \), is correct if these values hold true.
Ultimately, without the actual coordinates visible to determine \( A \) and \( M \), it’s suggested to select the option that fits logically with a vertical segment: R is located at \((-2, 2.5)\).
1 answer