Find midpoint M

Question

of the line segment with endpoints J(1.2,3.4)
and K(4.8,−2.3)
. If the solution includes a decimal, do not round.

(1 point)
The midpoint M
of segment JK¯¯¯¯¯¯¯¯
is at (
,
).

Answer 1

To find the midpoint \( M \) of a line segment with endpoints \( J(x_1, y_1) \) and \( K(x_2, y_2) \), we use the midpoint formula:

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

For the given points \( J(1.2, 3.4) \) and \( K(4.8, -2.3) \):

• \( x_1 = 1.2 \)
• \( y_1 = 3.4 \)
• \( x_2 = 4.8 \)
• \( y_2 = -2.3 \)

Now, we can calculate the coordinates of the midpoint \( M \):

1. Calculate the \( x \)-coordinate of the midpoint:

\[ \frac{x_1 + x_2}{2} = \frac{1.2 + 4.8}{2} = \frac{6.0}{2} = 3.0 \]

2. Calculate the \( y \)-coordinate of the midpoint:

\[ \frac{y_1 + y_2}{2} = \frac{3.4 + (-2.3)}{2} = \frac{3.4 - 2.3}{2} = \frac{1.1}{2} = 0.55 \]

Therefore, the midpoint \( M \) of segment \( JK \) is:

\[ M(3.0, 0.55) \]

So, the answer is:

The midpoint \( M \) of segment \( JK \) is at \( (3.0, 0.55) \).