Question content area left

Question

Part 1
Find the coordinates of the point seven 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 7 right parenthesisUpper B left parenthesis 11 comma 4 right parenthesis

x y graph
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Question content area right
Part 1
The coordinates of the point seven 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 seven tenths of the way from point A to point B, we can use the section formula in coordinate geometry.

Let point A be \((-3, -7)\) and point B be \((11, 4)\).

The formula for finding the coordinates of a point \( P(x, y) \) that divides the line segment connecting points \( A(x_1, y_1) \) and \( B(x_2, y_2) \) in the ratio \( m:n \) is given by:

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

In this case, we want to find the point that is \( \frac{7}{10} \) of the way from A to B. This means we can think of it as the ratio \( 7:3 \) (because \( 7+3=10 \)). That means \( m = 7 \) and \( n = 3 \).

Now plug in the coordinates of points A and B:

• \( x_1 = -3, y_1 = -7 \)
• \( x_2 = 11, y_2 = 4 \)

Now calculate the x-coordinate and y-coordinate:

\[ x = \frac{(7)(11) + (3)(-3)}{7 + 3} = \frac{77 - 9}{10} = \frac{68}{10} = 6.8 \]

\[ y = \frac{(7)(4) + (3)(-7)}{7 + 3} = \frac{28 - 21}{10} = \frac{7}{10} = 0.7 \]

So the coordinates of the point seven tenths of the way from A to B are:

\[ (6.8, 0.7) \]

Thus, the answer is: \[ \boxed{(6.8, 0.7)} \]