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What fraction of the way will you portion the directed line segment?

In what direction will you portion the directed line segment?

How many units horizontally will the new partitioned point move?

How many units, vertically will the new partitioned point move?

What is the coordinate of the point portioned in a ratio of 1 to 4 on the directed line segment?

What fraction of the way will you portion the directed line segment? In what direction-example-1
User Sqweek
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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:

User Spencer Ruport
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