Answer:
I can help you with some of the questions you asked. Here are my answers:
- To partition the directed line segment MN in the ratio of 1:4 from M to N, you will portion it at 1/5 or 20% of the way from M to N. This is because the ratio of 1:4 means that the line segment is divided into 5 equal parts, and the first part is 1/5 of the whole segment.
- The direction of the partitioning is the same as the direction of the line segment MN, which is from left to right and slightly upward. You can use a protractor to measure the angle of the line segment MN with respect to the horizontal axis, which is about 26.6 degrees.
- To find the horizontal distance that the new partitioned point moves, you can use the formula for finding the x-coordinate of a point on a line segment given by:
x = x1 + t(x2 - x1)
where x1 and x2 are the x-coordinates of the endpoints of the line segment, and t is the fraction of the way from the first endpoint to the second endpoint. In this case, x1 = 0, x2 = 10, and t = 1/5. Plugging these values into the formula, we get:
x = 0 + (1/5)(10 - 0)
x = 2
Therefore, the new partitioned point moves 2 units horizontally from M to N.
- To find the vertical distance that the new partitioned point moves, you can use a similar formula for finding the y-coordinate of a point on a line segment given by:
y = y1 + t(y2 - y1)
where y1 and y2 are the y-coordinates of the endpoints of the line segment, and t is the same fraction as before. In this case, y1 = 0, y2 = 5, and t = 1/5. Plugging these values into the formula, we get:
y = 0 + (1/5)(5 - 0)
y = 1
Therefore, the new partitioned point moves 1 unit vertically from M to N.
- The coordinate of the point portioned in a ratio of 1:4 on the directed line segment MN is (2,1), which is obtained by combining the x and y values calculated above.
I hope this helps you understand how to partition a directed line segment in a given ratio. If you have any other questions, please feel free to ask me.
Explanation: