Question
, how would adding 5 and -2, then dividing by 2 help you find the midpoint of the line segment %0D%0A%0D%0A%0D%0A%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0AIt finds the y-value that is the average between the two y-values of points %0D%0AIt finds the y-value that is the average between the two y-values of points %0D%0A%0D%0AIt finds the sole midpoint of points A and B%0D%0AIt finds the sole midpoint of points A and B%0D%0A%0D%0AIt finds the distance between points A and B%0D%0AIt finds the distance between points A and B%0D%0A%0D%0AIt finds the x-value that is the average between the two x-values of points
Answers
GPT-4o mini
To find the midpoint of a line segment defined by two points \( A(x_1, y_1) \) and \( B(x_2, y_2) \), you can use the midpoint formula:
\[
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]
If we consider the specific operation of adding \( 5 \) and \( -2 \), which represents the y-coordinates of two points on the line segment, you can see how this relates to finding the midpoint:
1. **Adding the y-values**: If \( 5 \) and \( -2 \) are the y-coordinates of the two points, you add these values: \( 5 + (-2) = 3 \).
2. **Dividing by 2**: Next, dividing this sum by 2 gives you the average: \( \frac{3}{2} = 1.5 \).
This result, \( 1.5 \), represents the y-coordinate of the midpoint of the line segment connecting the two points with y-coordinates \( 5 \) and \( -2 \).
Based on these explanations, the correct response is:
**It finds the y-value that is the average between the two y-values of points.**
\[
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]
If we consider the specific operation of adding \( 5 \) and \( -2 \), which represents the y-coordinates of two points on the line segment, you can see how this relates to finding the midpoint:
1. **Adding the y-values**: If \( 5 \) and \( -2 \) are the y-coordinates of the two points, you add these values: \( 5 + (-2) = 3 \).
2. **Dividing by 2**: Next, dividing this sum by 2 gives you the average: \( \frac{3}{2} = 1.5 \).
This result, \( 1.5 \), represents the y-coordinate of the midpoint of the line segment connecting the two points with y-coordinates \( 5 \) and \( -2 \).
Based on these explanations, the correct response is:
**It finds the y-value that is the average between the two y-values of points.**