Question

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 4 comma negative 5 right parenthesisUpper B left parenthesis 9 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 that is three tenths of the way from point A (-4, -5) to point B (9, 7), we can use the formula for finding a point that divides the line segment joining two points in a given ratio.

Let \( A = (-4, -5) \) and \( B = (9, 7) \).

The formula for finding a point that divides the segment joining \( A \) and \( B \) in the ratio \( m:n \) is given by:

\[
\left( \frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n} \right)
\]

In this case, we want the point that is \( \frac{3}{10} \) of the way from \( A \) to \( B \). This is equivalent to using the ratio \( m = 3 \) and \( n = 7 \) (since \( 7 \) is the remaining part of the segment).

So, we need to calculate the coordinates as follows:

\[
x = \frac{3 \cdot 9 + 7 \cdot (-4)}{3+7}
\]
\[
y = \frac{3 \cdot 7 + 7 \cdot (-5)}{3+7}
\]

Calculating \( x \):

\[
x = \frac{27 - 28}{10} = \frac{-1}{10} = -0.1
\]

Calculating \( y \):

\[
y = \frac{21 - 35}{10} = \frac{-14}{10} = -1.4
\]

Thus, the coordinates of the point that is three tenths of the way from \( A \) to \( B \) are \( (-0.1, -1.4) \).

So the final answer is:

\[
(-0.1, -1.4)
\]