Question

Find the midpoint
(1,-4)(-2,-7)

Answer 1

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

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

For the points \((1, -4)\) and \((-2, -7)\):

- \(x_1 = 1\)
- \(y_1 = -4\)
- \(x_2 = -2\)
- \(y_2 = -7\)

Now, substitute these values into the formula:

\[
\text{Midpoint} = \left( \frac{1 + (-2)}{2}, \frac{-4 + (-7)}{2} \right)
\]

Calculating each component:

1. For the x-coordinate:
\[
\frac{1 - 2}{2} = \frac{-1}{2} = -\frac{1}{2}
\]

2. For the y-coordinate:
\[
\frac{-4 - 7}{2} = \frac{-11}{2}
\]

So, the midpoint is:

\[
\left( -\frac{1}{2}, -\frac{11}{2} \right)
\]

Thus, the midpoint of the points \((1, -4)\) and \((-2, -7)\) is \(\left( -\frac{1}{2}, -\frac{11}{2} \right)\).