Question

find the missing endpoint if S is the midpoint RT
1) R(-9,4) and S(2,-11) find T
2) S(-4,-6) and T(-7,-3) find R

Answer 1

find the missing endpoint if S is the midpoint RT
1) R(-9,4) and S(2,-11) find T

Answer 2

To find the missing endpoint using the midpoint formula, you can use the following formula for the midpoint \( S \) of segment \( RT \):

\[
S = \left( \frac{x_R + x_T}{2}, \frac{y_R + y_T}{2} \right)
\]

### 1) Given:
- R(-9, 4)
- S(2, -11)

We need to find point T. We can set up the equations based on the midpoint formula:

\[
S_x = \frac{x_R + x_T}{2} \quad \text{and} \quad S_y = \frac{y_R + y_T}{2}
\]

Substituting the known values into the equations:

For the x-coordinates:
\[
2 = \frac{-9 + x_T}{2}
\]
Multiply both sides by 2:
\[
4 = -9 + x_T
\]
Adding 9 to both sides:
\[
x_T = 13
\]

For the y-coordinates:
\[
-11 = \frac{4 + y_T}{2}
\]
Multiply both sides by 2:
\[
-22 = 4 + y_T
\]
Subtracting 4 from both sides:
\[
y_T = -26
\]

So, the missing endpoint T is:
\[
T(13, -26)
\]


### 2) Given:
- S(-4, -6)
- T(-7, -3)

We need to find point R. Again, we can use the midpoint formula:

For the x-coordinates:
\[
-4 = \frac{x_R + (-7)}{2}
\]
Multiply both sides by 2:
\[
-8 = x_R - 7
\]
Adding 7 to both sides:
\[
x_R = -1
\]

For the y-coordinates:
\[
-6 = \frac{y_R + (-3)}{2}
\]
Multiply both sides by 2:
\[
-12 = y_R - 3
\]
Adding 3 to both sides:
\[
y_R = -9
\]

So, the missing endpoint R is:
\[
R(-1, -9)
\]

### Summary:
1. T is (13, -26)
2. R is (-1, -9)

Answer 3

To find the missing endpoint \( T \) when \( S \) is the midpoint of segment \( RT \), we can use the midpoint formula:

\[
S = \left( \frac{x_R + x_T}{2}, \frac{y_R + y_T}{2} \right)
\]

Given:
- \( R(-9, 4) \)
- \( S(2, -11) \)

We need to find point \( T(x_T, y_T) \).

### Step 1: Set up the equations using the midpoint formula

1. For the x-coordinates:
\[
2 = \frac{-9 + x_T}{2}
\]

2. For the y-coordinates:
\[
-11 = \frac{4 + y_T}{2}
\]

### Step 2: Solve for \( x_T \)

Starting with the x-coordinate:
\[
2 = \frac{-9 + x_T}{2}
\]
Multiply both sides by 2:
\[
4 = -9 + x_T
\]
Add 9 to both sides:
\[
x_T = 4 + 9 = 13
\]

### Step 3: Solve for \( y_T \)

Now for the y-coordinate:
\[
-11 = \frac{4 + y_T}{2}
\]
Multiply both sides by 2:
\[
-22 = 4 + y_T
\]
Subtract 4 from both sides:
\[
y_T = -22 - 4 = -26
\]

### Conclusion

The missing endpoint \( T \) is:
\[
T(13, -26)
\]