Question

Question

Use the image to answer the question.

A line segment on a coordinate plane. Both the x-and y-axes range from negative 3 to 4 in unit increments. The line segment descends from upper A on the top left to upper B on the bottom right.

Find midpoint M
of the line segment with endpoints A(−1.4,2.5)
and B(2.6,−1.5)
. Enter both responses as a decimal value to the tenth place.

(1 point)
The midpoint of segment AB¯¯¯¯¯¯¯¯
is (
,
).

Answer 1

To find the midpoint \( M \) of the line segment with endpoints \( A(-1.4, 2.5) \) and \( B(2.6, -1.5) \), you can use the midpoint formula:

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

Where \( (x_1, y_1) \) are the coordinates of point \( A \) and \( (x_2, y_2) \) are the coordinates of point \( B \).

Substituting in the coordinates of points \( A \) and \( B \):

\[ x_1 = -1.4, \quad y_1 = 2.5 \] \[ x_2 = 2.6, \quad y_2 = -1.5 \]

Now, calculate the \( x \)-coordinate of the midpoint:

\[ x_M = \frac{-1.4 + 2.6}{2} = \frac{1.2}{2} = 0.6 \]

Now, calculate the \( y \)-coordinate of the midpoint:

\[ y_M = \frac{2.5 + (-1.5)}{2} = \frac{1.0}{2} = 0.5 \]

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

\[ M(0.6, 0.5) \]

Therefore, the final answer is:

The midpoint of segment \( AB \) is \( (0.6, 0.5) \).