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 4 comma negative 5 right parenthesisUpper B left parenthesis 12 comma 6 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 \( A \) to point \( B \), we can use the formula for finding a point along the line segment connecting two points. The formula to determine the coordinates \( P(x, y) \) that divides the segment \( AB \) in the ratio \( m:n \) is given by:

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

In this case:

• Point \( A(-4, -5) \) (denoted as \( (x_1, y_1) \))
• Point \( B(12, 6) \) (denoted as \( (x_2, y_2) \))
• You want to find the point \( P \) that is \( \frac{3}{10} \) of the way from \( A \) to \( B \). This means it is \( 3 \) parts towards \( B \) and \( 7 \) parts towards \( A \). Thus, the ratio \( m:n = 3:7 \).

Now we can plug in the values into the formula:

1. Calculate for the x-coordinate: \[ x = \frac{3(12) + 7(-4)}{3 + 7} = \frac{36 - 28}{10} = \frac{8}{10} = 0.8 \]

2. Calculate for the y-coordinate: \[ y = \frac{3(6) + 7(-5)}{3 + 7} = \frac{18 - 35}{10} = \frac{-17}{10} = -1.7 \]

Combining the two results, the coordinates of the point three-tenths of the way from \( A \) to \( B \) are:

\[ \boxed{(0.8, -1.7)} \]