Point C ( 1,2) and point D ( 7,10) lie in the standard coordiant plane . What are the coordinates of the midpoints of `bar (CD) `

Options

A. (1,8)
B. `(3,-6)`
C. `(4,-4)`
D. `(4,-6)`

Answer

To find the coordinates of the midpoint of the line segment joining points C and D, we can follow these steps:

### Step 1: Identify the coordinates of points C and D
The coordinates of point C are (1, 2) and the coordinates of point D are (7, 10).

### Step 2: Use the midpoint formula
The formula for finding the midpoint M of a line segment joining two points (x₁, y₁) and (x₂, y₂) is given by:
\[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]

### Step 3: Substitute the coordinates into the formula
Here, we have:
- \(x_1 = 1\), \(y_1 = 2\)
- \(x_2 = 7\), \(y_2 = 10\)

Substituting these values into the midpoint formula:
\[ M = \left( \frac{1 + 7}{2}, \frac{2 + 10}{2} \right) \]

### Step 4: Calculate the x-coordinate of the midpoint
Calculating the x-coordinate:
\[ \frac{1 + 7}{2} = \frac{8}{2} = 4 \]

### Step 5: Calculate the y-coordinate of the midpoint
Calculating the y-coordinate:
\[ \frac{2 + 10}{2} = \frac{12}{2} = 6 \]

### Step 6: Write the coordinates of the midpoint
Thus, the coordinates of the midpoint M are:
\[ M = (4, 6) \]

### Final Answer
The coordinates of the midpoint of line segment CD are (4, 6).

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