Westonci.ca is your go-to source for answers, with a community ready to provide accurate and timely information. Explore a wealth of knowledge from professionals across different disciplines on our comprehensive platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.
Sagot :
Sure! Let's determine the coordinates of two points on the line segment joining points A (4, -1) and B (4, 5).
### Step-by-Step Solution:
1. Determine the Midpoint of Segment AB:
To find the midpoint between two points, we use the midpoint formula:
\( \text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \)
For our points A (4, -1) and B (4, 5):
- The x-coordinate of the midpoint is \( \frac{4 + 4}{2} = 4.0 \)
- The y-coordinate of the midpoint is \( \frac{-1 + 5}{2} = 2.0 \)
So, the coordinates of the midpoint are \( (4.0, 2.0) \).
2. Determine a Point Located One-Third of the Distance from A to B:
To find a point that divides the segment in a given ratio, say \( m:n \), we use the section formula:
\( P = \left( \frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n} \right) \)
For a point one-third of the way from A to B (or dividing the segment in the ratio 1:2):
- The x-coordinate remains 4 because the x-coordinates of both points are the same.
- The y-coordinate is given by \( \frac{1 \cdot 5 + 2 \cdot (-1)}{1 + 2} = \frac{5 - 2}{3} = 1.0 \)
Thus, the coordinates of the point one-third of the distance from A to B are \( (4, 1.0) \).
### Final Coordinates:
- Midpoint: \( (4.0, 2.0) \)
- One-third Point: \( (4, 1.0) \)
These are the coordinates of two points on the line segment joining A (4, -1) and B (4, 5).
### Step-by-Step Solution:
1. Determine the Midpoint of Segment AB:
To find the midpoint between two points, we use the midpoint formula:
\( \text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \)
For our points A (4, -1) and B (4, 5):
- The x-coordinate of the midpoint is \( \frac{4 + 4}{2} = 4.0 \)
- The y-coordinate of the midpoint is \( \frac{-1 + 5}{2} = 2.0 \)
So, the coordinates of the midpoint are \( (4.0, 2.0) \).
2. Determine a Point Located One-Third of the Distance from A to B:
To find a point that divides the segment in a given ratio, say \( m:n \), we use the section formula:
\( P = \left( \frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n} \right) \)
For a point one-third of the way from A to B (or dividing the segment in the ratio 1:2):
- The x-coordinate remains 4 because the x-coordinates of both points are the same.
- The y-coordinate is given by \( \frac{1 \cdot 5 + 2 \cdot (-1)}{1 + 2} = \frac{5 - 2}{3} = 1.0 \)
Thus, the coordinates of the point one-third of the distance from A to B are \( (4, 1.0) \).
### Final Coordinates:
- Midpoint: \( (4.0, 2.0) \)
- One-third Point: \( (4, 1.0) \)
These are the coordinates of two points on the line segment joining A (4, -1) and B (4, 5).
Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.