Question

Question content area left
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.)

Answer 1

To 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:
- \( A(-3, -8) \)
- \( B(10, 7) \)

To find the coordinates of the point \( P \) that is \( \frac{3}{10} \) of the way from \( A \) to \( B \), we can use the section formula:

\[
P = \left( \frac{x_1 + m \cdot x_2}{m + n}, \frac{y_1 + m \cdot y_2}{m + n} \right)
\]

Here, \( m \) is the ratio of the distances from \( A \) to \( P \) (3), and \( n \) is the ratio of the distances from \( P \) to \( B \) (7), because \( 10 - 3 = 7 \).

Thus, substituting the coordinates of A and B gives:

\[
P = \left( \frac{-3 + 3 \cdot 10}{3 + 7}, \frac{-8 + 3 \cdot 7}{3 + 7} \right)
\]

Calculating the x-coordinate:

\[
P_x = \frac{-3 + 30}{10} = \frac{27}{10} = 2.7
\]

Calculating the y-coordinate:

\[
P_y = \frac{-8 + 21}{10} = \frac{13}{10} = 1.3
\]

Thus, the coordinates of the point three tenths of the way from A to B are:

\[
\left(2.7, 1.3\right)
\]

So the final answer is:

**The coordinates of the point three tenths of the way from A to B are \( (2.7, 1.3) \).**