Question

Given the endpoints G(0.4,0.8)
and H(3.9,−1.4)
, calculate the location of midpoint M
.

Answer 1

To find the midpoint \( M \) of the line segment with endpoints \( G(x_1, y_1) \) and \( H(x_2, y_2) \), you can use the midpoint formula:

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

Given the endpoints:
- \( G(0.4, 0.8) \) where \( x_1 = 0.4 \) and \( y_1 = 0.8 \)
- \( H(3.9, -1.4) \) where \( x_2 = 3.9 \) and \( y_2 = -1.4 \)

Now, plug these values into the midpoint formula:

\[
M\left(\frac{0.4 + 3.9}{2}, \frac{0.8 + (-1.4)}{2}\right)
\]

Calculating the \( x \)-coordinate:

\[
\frac{0.4 + 3.9}{2} = \frac{4.3}{2} = 2.15
\]

Now calculating the \( y \)-coordinate:

\[
\frac{0.8 + (-1.4)}{2} = \frac{0.8 - 1.4}{2} = \frac{-0.6}{2} = -0.3
\]

Thus, the coordinates of the midpoint \( M \) are:

\[
M(2.15, -0.3)
\]

So, the location of the midpoint \( M \) is \( (2.15, -0.3) \).