The Midpoint Formula Worksheet | PDF - Free Printable

The user wants me to solve the math problems presented in the image.

Task Analysis:
1. Identify the goal: The worksheet asks to find the midpoints for 7 pairs of coordinates.
2. Understand the method: The formula is provided: Midpoint = $(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})$. This means I need to average the x-values and average the y-values for each pair.
3. Process each problem:
* Problem 1: Endpoints $(10, 7)$ and $(10, 5)$.
* $x_{mid} = \frac{10 + 10}{2} = 10$
* $y_{mid} = \frac{7 + 5}{2} = 6$
* Midpoint: $(10, 6)$
* Problem 2: Endpoints $(-1, 1)$ and $(1, 5)$.
* $x_{mid} = \frac{-1 + 1}{2} = 0$
* $y_{mid} = \frac{1 + 5}{2} = 3$
* Midpoint: $(0, 3)$
* Problem 3: Endpoints $(-5, -7)$ and $(-8, -1)$.
* $x_{mid} = \frac{-5 + (-8)}{2} = \frac{-13}{2} = -6.5$
* $y_{mid} = \frac{-7 + (-1)}{2} = \frac{-8}{2} = -4$
* Midpoint: $(-6.5, -4)$
* Problem 4: Endpoints $(0, 7)$ and $(10, 7)$.
* $x_{mid} = \frac{0 + 10}{2} = 5$
* $y_{mid} = \frac{7 + 7}{2} = 7$
* Midpoint: $(5, 7)$
* Problem 5: Endpoints $(-1, 1)$ and $(-5, -7)$.
* $x_{mid} = \frac{-1 + (-5)}{2} = \frac{-6}{2} = -3$
* $y_{mid} = \frac{1 + (-7)}{2} = \frac{-6}{2} = -3$
* Midpoint: $(-3, -3)$
* Problem 6: Endpoints $(-7, 1)$ and $(-5, -3)$.
* $x_{mid} = \frac{-7 + (-5)}{2} = \frac{-12}{2} = -6$
* $y_{mid} = \frac{1 + (-3)}{2} = \frac{-2}{2} = -1$
* Midpoint: $(-6, -1)$
* Problem 7: Endpoints $(1, 5)$ and $(10, 5)$.
* $x_{mid} = \frac{1 + 10}{2} = \frac{11}{2} = 5.5$
* $y_{mid} = \frac{5 + 5}{2} = 5$
* Midpoint: $(5.5, 5)$

Verification:
1. $(10+10)/2 = 10$, $(7+5)/2 = 6$. Correct.
2. $(-1+1)/2 = 0$, $(1+5)/2 = 3$. Correct.
3. $(-5-8)/2 = -6.5$, $(-7-1)/2 = -4$. Correct.
4. $(0+10)/2 = 5$, $(7+7)/2 = 7$. Correct.
5. $(-1-5)/2 = -3$, $(1-7)/2 = -3$. Correct.
6. $(-7-5)/2 = -6$, $(1-3)/2 = -1$. Correct.
7. $(1+10)/2 = 5.5$, $(5+5)/2 = 5$. Correct.

The prompt asks for the solution to the task. The task is to fill in the "Midpoint" column for the 7 problems. I will list the solutions clearly. Since "ExplainAnswer" is false, I will skip the detailed explanation section and go straight to the reasoning and then the final answer block. Wait, looking at the options:
- ExplainAnswer: false
- TeachTopic: false
- GeneratePractice: false

This means I just need to provide the Final Answer. However, the instructions say "Complete ALL reasoning and explanations BEFORE writing the Final Answer." This implies I should show my work/reasoning in the main body, but since the specific "Explanation" section is disabled, I will just present the calculations clearly as part of the standard response flow leading up to the final answer.

Actually, re-reading the "Response format rules": "If an option is false, completely omit that section."
So I will omit the "Explanation:", "Teach the Topic:", and "Practice Task:" headers.
I will write out the step-by-step calculations in the main body text to satisfy the "Complete ALL reasoning... BEFORE writing the Final Answer" rule, and then put the summarized results in the Final Answer section.

Let's double check the calculations.
1. $(10, 7), (10, 5) \rightarrow (\frac{20}{2}, \frac{12}{2}) = (10, 6)$
2. $(-1, 1), (1, 5) \rightarrow (\frac{0}{2}, \frac{6}{2}) = (0, 3)$
3. $(-5, -7), (-8, -1) \rightarrow (\frac{-13}{2}, \frac{-8}{2}) = (-6.5, -4)$
4. $(0, 7), (10, 7) \rightarrow (\frac{10}{2}, \frac{14}{2}) = (5, 7)$
5. $(-1, 1), (-5, -7) \rightarrow (\frac{-6}{2}, \frac{-6}{2}) = (-3, -3)$
6. $(-7, 1), (-5, -3) \rightarrow (\frac{-12}{2}, \frac{-2}{2}) = (-6, -1)$
7. $(1, 5), (10, 5) \rightarrow (\frac{11}{2}, \frac{10}{2}) = (5.5, 5)$

Everything looks solid. I will present the final list.

One detail: Problem 3 results in a decimal. The example in the image uses decimals ($(-2.5, 2)$), so decimals are acceptable. Fractions like $11/2$ or $-13/2$ are also mathematically correct, but decimals are consistent with the example. I'll provide decimals.

Final Answer format: Just the list of answers corresponding to numbers 1-7.

1. $(10, 6)$
2. $(0, 3)$
3. $(-6.5, -4)$
4. $(5, 7)$
5. $(-3, -3)$
6. $(-6, -1)$
7. $(5.5, 5)$

I will write out the steps clearly.
Step 1: Formula is $(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$.
Step 2: Apply to each pair.
... calculations ...
Step 3: Compile results.

Ready to write.
To find the midpoint between two points, you use the formula provided in the worksheet:
$$\text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$$

This means you add the x-coordinates together and divide by 2, then do the same for the y-coordinates. Here is the step-by-step calculation for each problem:

1. Endpoints: $(10, 7)$ and $(10, 5)$
* $x$-coordinate: $(10 + 10) / 2 = 20 / 2 = 10$
* $y$-coordinate: $(7 + 5) / 2 = 12 / 2 = 6$
* Midpoint: $(10, 6)$

2. Endpoints: $(-1, 1)$ and $(1, 5)$
* $x$-coordinate: $(-1 + 1) / 2 = 0 / 2 = 0$
* $y$-coordinate: $(1 + 5) / 2 = 6 / 2 = 3$
* Midpoint: $(0, 3)$

3. Endpoints: $(-5, -7)$ and $(-8, -1)$
* $x$-coordinate: $(-5 + -8) / 2 = -13 / 2 = -6.5$
* $y$-coordinate: $(-7 + -1) / 2 = -8 / 2 = -4$
* Midpoint: $(-6.5, -4)$

4. Endpoints: $(0, 7)$ and $(10, 7)$
* $x$-coordinate: $(0 + 10) / 2 = 10 / 2 = 5$
* $y$-coordinate: $(7 + 7) / 2 = 14 / 2 = 7$
* Midpoint: $(5, 7)$

5. Endpoints: $(-1, 1)$ and $(-5, -7)$
* $x$-coordinate: $(-1 + -5) / 2 = -6 / 2 = -3$
* $y$-coordinate: $(1 + -7) / 2 = -6 / 2 = -3$
* Midpoint: $(-3, -3)$

6. Endpoints: $(-7, 1)$ and $(-5, -3)$
* $x$-coordinate: $(-7 + -5) / 2 = -12 / 2 = -6$
* $y$-coordinate: $(1 + -3) / 2 = -2 / 2 = -1$
* Midpoint: $(-6, -1)$

7. Endpoints: $(1, 5)$ and $(10, 5)$
* $x$-coordinate: $(1 + 10) / 2 = 11 / 2 = 5.5$
* $y$-coordinate: $(5 + 5) / 2 = 10 / 2 = 5$
* Midpoint: $(5.5, 5)$

Final Answer:
1. $(10, 6)$
2. $(0, 3)$
3. $(-6.5, -4)$
4. $(5, 7)$
5. $(-3, -3)$
6. $(-6, -1)$
7. $(5.5, 5)$