Question

find the coordinates of the midpoint of the segment given its endpoint
1) A(5,8) and B(-1,-4)
2) M(-5,9) and N(-2,7)

Answer 1

dumb it down

Answer 2

Midpoint of M and N is \(\left( -\frac{7}{2}, 8 \right)\).

Answer 3

find the coordinates of the midpoint of the segment given its endpoint
1) P (-3,-7) and Q(3,-5)
2) F(2,-6) and G(-8,5)

Answer 4

To find the coordinates of the midpoint of a line segment given its endpoints, you can use the midpoint formula:

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

where \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of the endpoints.

### 1) For endpoints A(5, 8) and B(-1, -4):

- \(x_1 = 5\), \(y_1 = 8\) (for point A)
- \(x_2 = -1\), \(y_2 = -4\) (for point B)

Using the midpoint formula:

\[
M = \left( \frac{5 + (-1)}{2}, \frac{8 + (-4)}{2} \right) = \left( \frac{4}{2}, \frac{4}{2} \right) = (2, 2)
\]

So, the midpoint of segment AB is \(M(2, 2)\).

### 2) For endpoints M(-5, 9) and N(-2, 7):

- \(x_1 = -5\), \(y_1 = 9\) (for point M)
- \(x_2 = -2\), \(y_2 = 7\) (for point N)

Using the midpoint formula:

\[
M = \left( \frac{-5 + (-2)}{2}, \frac{9 + 7}{2} \right) = \left( \frac{-7}{2}, \frac{16}{2} \right) = \left( -\frac{7}{2}, 8 \right)
\]

So, the midpoint of segment MN is \(M\left(-\frac{7}{2}, 8\right)\).

### Summary of Midpoints:
1) Midpoint of segment AB is \(M(2, 2)\).
2) Midpoint of segment MN is \(M\left(-\frac{7}{2}, 8\right)\).

Answer 5

Sure! Let’s break it down step by step in very simple terms.

### 1) Finding the Midpoint of A(5, 8) and B(-1, -4)

**Step 1:** Add the x-coordinates together:
\(5 + (-1) = 4\)

**Step 2:** Divide that sum by 2:
\(\frac{4}{2} = 2\) (this is the x-coordinate of the midpoint)

**Step 3:** Now do the same for the y-coordinates:
\(8 + (-4) = 4\)

**Step 4:** Divide that sum by 2:
\(\frac{4}{2} = 2\) (this is the y-coordinate of the midpoint)

**Result:** The midpoint between A and B is \( (2, 2) \).

---

### 2) Finding the Midpoint of M(-5, 9) and N(-2, 7)

**Step 1:** Add the x-coordinates together:
\(-5 + (-2) = -7\)

**Step 2:** Divide that sum by 2:
\(\frac{-7}{2} = -\frac{7}{2}\) (this is the x-coordinate of the midpoint)

**Step 3:** Now do the same for the y-coordinates:
\(9 + 7 = 16\)

**Step 4:** Divide that sum by 2:
\(\frac{16}{2} = 8\) (this is the y-coordinate of the midpoint)

**Result:** The midpoint between M and N is \(\left( -\frac{7}{2}, 8 \right)\).

---

### Final Answers:
1) Midpoint of A and B is \( (2, 2) \).
2) Midpoint of M and N is \(\left( -\frac{7}{2}, 8 \right)\).

Answer 6

Let's clarify the midpoint of points M and N again for accuracy.

We have the points:

- M(-5, 9)
- N(-2, 7)

**Step 1:** Add the x-coordinates:
\[
-5 + (-2) = -7
\]

**Step 2:** Divide by 2 to get the x-coordinate of the midpoint:
\[
\frac{-7}{2} = -\frac{7}{2}
\]

**Step 3:** Now add the y-coordinates:
\[
9 + 7 = 16
\]

**Step 4:** Divide by 2 to get the y-coordinate of the midpoint:
\[
\frac{16}{2} = 8
\]

So, the midpoint of points M and N is indeed:
\[
\left( -\frac{7}{2}, 8 \right)
\]

If you have any further questions or if something doesn’t seem right, feel free to ask!

Answer 7

To find the midpoint of a line segment given its endpoints, we can use the midpoint formula:

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

where \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of the endpoints.

### 1) Finding the Midpoint of P(-3, -7) and Q(3, -5)

- For point P: \(x_1 = -3\), \(y_1 = -7\)
- For point Q: \(x_2 = 3\), \(y_2 = -5\)

Using the midpoint formula:

\[
M = \left( \frac{-3 + 3}{2}, \frac{-7 + (-5)}{2} \right) = \left( \frac{0}{2}, \frac{-12}{2} \right) = (0, -6)
\]

**Result:** The midpoint of segment PQ is \(M(0, -6)\).

---

### 2) Finding the Midpoint of F(2, -6) and G(-8, 5)

- For point F: \(x_1 = 2\), \(y_1 = -6\)
- For point G: \(x_2 = -8\), \(y_2 = 5\)

Using the midpoint formula:

\[
M = \left( \frac{2 + (-8)}{2}, \frac{-6 + 5}{2} \right) = \left( \frac{-6}{2}, \frac{-1}{2} \right) = (-3, -0.5)
\]

**Result:** The midpoint of segment FG is \(M(-3, -0.5)\).

### Final Answers:
1) Midpoint of segment PQ is \(M(0, -6)\).
2) Midpoint of segment FG is \(M(-3, -0.5)\).