Question content area left

Part 1
Find the coordinates of the point three tenths
of the way from A to B.
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-4
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-10
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x
y
Upper Aleft parenthesis negative 3 comma negative 8 right parenthesisUpper B left parenthesis 10 comma 7 right parenthesis

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Question content area right
Part 1
The coordinates of the point three tenths
of the way from A to B are
  
enter your response here.
​(Type an ordered​ pair.)

1 answerTo find the coordinates of the point three tenths of the way from point A to point B, you can use the formula for finding a point that divides the line segment between two points in a specified ratio.Points A and B are defined as:To find the coordinates of the point that is of the way from to , we can use the section formula: Here, is the ratio of the distances from to (3), and is the ratio of the distances from to (7), because .Thus, substituting the coordinates of A and B gives: Calculating the x-coordinate: Calculating the y-coordinate: Thus, the coordinates of the point three tenths of the way from A to B are:So the final answer is:The coordinates of the point three tenths of the way from A to B are .That's incorrect.
Find three tenths
of the horizontal and vertical distances from A to B. Add the horizontal distance to the​ x-coordinate and the vertical distance to the​ y-coordinate of point A.

1 answer

To find the coordinates of the point that is three-tenths of the way from point A to point B, we can follow these steps.

Given:

  • Point A: A(3,8)
  • Point B: B(10,7)
  1. Find the difference in x-coordinates and y-coordinates: Δx=xBxA=10(3)=10+3=13 Δy=yByA=7(8)=7+8=15

  2. Calculate three-tenths of the way: Distance in x=310×Δx=310×13=3.9 Distance in y=310×Δy=310×15=4.5

  3. Add these distances to the coordinates of point A: x=xA+Distance in x=3+3.9=0.9 y=yA+Distance in y=8+4.5=3.5

Thus, the coordinates of the point that is three-tenths of the way from A to B are: (0.9,3.5)