If $$ \mathrm{P}=(3,1) $$ and $$ \mathrm{Q}=(-3,-7) $$, find the midpoint of segment PQ . ([ ? ],[ ])

Question

UpStudy AI · Accepted Answer

To find the midpoint $$ M $$ of the segment $$ PQ $$ with endpoints $$ P(3, 1) $$ and $$ Q(-3, -7) $$, we 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 $$ P $$ and $$ (x_2, y_2) $$ are the coordinates of point $$ Q $$.

Substituting the coordinates of points $$ P $$ and $$ Q $$:

- $$ x_1 = 3 $$
- $$ y_1 = 1 $$
- $$ x_2 = -3 $$
- $$ y_2 = -7 $$

Now, we can calculate the midpoint:

$$
M = \left( \frac{3 + (-3)}{2}, \frac{1 + (-7)}{2} \right)
$$

Calculating each component:

1. For the x-coordinate:
   $$
   \frac{3 - 3}{2} = \frac{0}{2} = 0
   $$

2. For the y-coordinate:
   $$
   \frac{1 - 7}{2} = \frac{-6}{2} = -3
   $$

Thus, the midpoint $$ M $$ is:

$$
M = (0, -3)
$$

Therefore, the midpoint of segment $$ PQ $$ is $$[0, -3]$$.
The midpoint of segment $$ PQ $$ is $$[0, -3]$$.

If \( \mathrm{P}=(3,1) \) and \( \mathrm{Q}=(-3,-7) \), find the midpoint of segment PQ . ([ ? ],[ ])