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
4
6
8
10
12
14
-10
-8
-6
-4
-2
2
4
6
8
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: \[ \Delta x = x_B - x_A = 10 - (-3) = 10 + 3 = 13 \] \[ \Delta y = y_B - y_A = 7 - (-8) = 7 + 8 = 15 \]

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

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: \[ \boxed{(0.9, -3.5)} \]