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).