Question

The roof of a house is represented on the coordinate plane below.
graph shows point a (-7,-2) and point b (5,4)


A builder attaches a support beam to the roof, at a point exactly half of the way between point A and point B .

What are the coordinates of that point? Drag and drop numbers into the boxes to correctly complete the coordinates.



(2 points)

Answer 1

To find the point exactly halfway between point A (-7, -2) and point B (5, 4), we will use the midpoint formula. The midpoint \( M \) of two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

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

Here, \((x_1, y_1) = (-7, -2)\) and \((x_2, y_2) = (5, 4)\).

Now, we can calculate the midpoint:

1. Calculate the x-coordinate:
\[
\frac{-7 + 5}{2} = \frac{-2}{2} = -1
\]

2. Calculate the y-coordinate:
\[
\frac{-2 + 4}{2} = \frac{2}{2} = 1
\]

Thus, the coordinates of the midpoint are \((-1, 1)\).

So you would drag and drop:

- The first box: -1
- The second box: 1

The coordinates of the point exactly halfway between point A and point B are \((-1, 1)\).