Question content area left

Question

Part 1
Find the coordinates of the point three tenths
of the way from A to B.
-6
-4
-2
2
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8
10
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-10
-8
-6
-4
-2
2
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10
x
y
Upper Aleft parenthesis negative 3 comma negative 8 right parenthesisUpper B left parenthesis 10 comma 7 right parenthesis

x y graph
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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.

Answer 1

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: $$\mathrm{\Delta }x=x_B-x_A=10-(-3)=10+3=13$$ $$\mathrm{\Delta }y=y_B-y_A=7-(-8)=7+8=15$$

2. Calculate three-tenths of the way: $$\text{Distance in x}=\frac{3}{10}\times \mathrm{\Delta }x=\frac{3}{10}\times 13=3.9$$ $$\text{Distance in y}=\frac{3}{10}\times \mathrm{\Delta }y=\frac{3}{10}\times 15=4.5$$

3. Add these distances to the coordinates of point A: $$x=x_A+\text{Distance in x}=-3+3.9=0.9$$ $$y=y_A+\text{Distance in y}=-8+4.5=-3.5$$

Thus, the coordinates of the point that is three-tenths of the way from A to B are: $$\boxed{{\displaystyle (0.9,-3.5)}}$$