Question

What is the midpoint between point A and B if point A is at (7,4) and point B is at (-9, 5). (1 point)

(-1, 9/2

ㅇ (8, 1/2

ㅇ (8, 9/2

(-1, 1/2

Answer 1

Use the substitution method to solve the system 2x + 3y = 4,4x6y-8. (1 point)

Ono solution

Ο (2-1)

infinite solutions

Ο (-1,2)

Answer 2

To find the midpoint between two points \( A(x_1, y_1) \) and \( B(x_2, y_2) \), you can use the midpoint formula:

\[
\text{Midpoint} \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]

Given point \( A (7, 4) \) and point \( B (-9, 5) \):

- \( x_1 = 7 \)
- \( y_1 = 4 \)
- \( x_2 = -9 \)
- \( y_2 = 5 \)

Now, calculate the x-coordinate of the midpoint:

\[
\frac{7 + (-9)}{2} = \frac{7 - 9}{2} = \frac{-2}{2} = -1
\]

Next, calculate the y-coordinate of the midpoint:

\[
\frac{4 + 5}{2} = \frac{9}{2}
\]

Hence, the midpoint between point A and point B is:

\[
\text{Midpoint} = (-1, \frac{9}{2})
\]

The correct answer is \( (-1, \frac{9}{2}) \).

Answer 3

There seems to be a typographical error in the second equation you provided. The equation "4x6y-8" is ambiguous. I assume you meant to write it in a more standard form.

Let's assume the system of equations is:

1. \( 2x + 3y = 4 \)
2. \( 4x + 6y = -8 \)

To apply the substitution method, we first solve the first equation for one variable. Let's solve for \( y \):

From the first equation:
\[
2x + 3y = 4 \implies 3y = 4 - 2x \implies y = \frac{4 - 2x}{3}
\]

Now, substitute \( y \) into the second equation. This will give us:

\[
4x + 6\left(\frac{4 - 2x}{3}\right) = -8
\]

Next, simplify the equation:

\[
4x + \frac{24 - 12x}{3} = -8
\]

Multiply everything by 3 to eliminate the fraction:

\[
3(4x) + 24 - 12x = -24
\]

This simplifies to:

\[
12x + 24 - 12x = -24
\]

The terms \( 12x \) and \( -12x \) cancel out:

\[
24 = -24
\]

This is a contradiction, which means there are no solutions to the system of equations.

Therefore, the correct answer is **no solution**.