Question

The coordinates of the midpoint of segment M N are 4 comma 1. The coordinates of point M are negative 2 comma 5. What are the coordinates of point N?Answer options with 5 optionsA.the point negative 8 comma 9B.the point 1 comma 3C.the point 4 comma 3D.the point 8 comma negative 5E.the point 10 comma negative 3

Answer 1

To find the coordinates of point N, we can use the formula for the midpoint of a segment, which is given by:

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

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

Given:
- Midpoint \( M N = (4, 1) \)
- Coordinates of point \( M = (-2, 5) \)

Let the coordinates of point N be \( (x_2, y_2) \).

Using the midpoint formula, we can set up the following equations:

1. For the x-coordinates:
\[
\frac{-2 + x_2}{2} = 4
\]

2. For the y-coordinates:
\[
\frac{5 + y_2}{2} = 1
\]

Now we can solve these equations step-by-step.

**For the x-coordinates:**

\[
\frac{-2 + x_2}{2} = 4
\]

Multiplying both sides by 2:

\[
-2 + x_2 = 8
\]

Adding 2 to both sides:

\[
x_2 = 10
\]

**For the y-coordinates:**

\[
\frac{5 + y_2}{2} = 1
\]

Multiplying both sides by 2:

\[
5 + y_2 = 2
\]

Subtracting 5 from both sides:

\[
y_2 = 2 - 5 = -3
\]

Thus, the coordinates of point N are \( (10, -3) \).

The correct answer is:
**E. the point (10, -3)**.