1.3-Midpoi X → C D sd206.org bookmarks Nicki Minaj X Messenger X Supreme Court Cas... Be Facebook X deltamath.com/app/student/solve/17127088/custom1665060425309 New Tab Start over Find the midpoint of points A(-6, 6) and B(2, 10) graphically. You may press submit or click the graph again to replot the midpoint. Remove Rectangle DeltaMath X E Edulastic: F X 5 4 y O 2 3 4 TextNow X M Inbox (18) X b Success C X < ☆ +

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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**Title: Finding the Midpoint of Two Points Graphically**

Here’s how you can visually find the midpoint of two points \( A(-6, 6) \) and \( B(2, 10) \).

### Instructions:

1. **Locate Points**:
   - Point \( A \) is positioned at \( (-6, 6) \) on the coordinate plane.
   - Point \( B \) is positioned at \( (2, 10) \).

2. **Graph Explanation**:
   - The graph displays a coordinate grid with both points \( A \) and \( B \) marked.
   - A line appears connecting the points \( A \) and \( B \) with a dotted rectangle outlining the vertical and horizontal segments between these points.

3. **Animating the Midpoint**:
   - Start by visualizing a right triangle formed from the x and y differences between the points.
   - Calculate the midpoint by using the midpoint formula: 
     \[
     \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
     \]
   - In this example, calculate:
     \[
     x\text{-coordinate}: \frac{-6 + 2}{2} = -2
     \]
     \[
     y\text{-coordinate}: \frac{6 + 10}{2} = 8
     \]

4. **Interactive Features**:
   - Click "Start over" to reset the graph or replot the midpoint.
   - Use the "Remove Rectangle" button to clear the rectangle.

5. **Submit Your Answer**:
   - Enter the calculated midpoint coordinates \( (-2, 8) \) in the provided fields.
   - Click "Submit Answer" to check your solution.

### Additional Information:
This method helps students grasp the geometric interpretation of finding midpoints, reinforcing the understanding through a visual and interactive approach.
Transcribed Image Text:**Title: Finding the Midpoint of Two Points Graphically** Here’s how you can visually find the midpoint of two points \( A(-6, 6) \) and \( B(2, 10) \). ### Instructions: 1. **Locate Points**: - Point \( A \) is positioned at \( (-6, 6) \) on the coordinate plane. - Point \( B \) is positioned at \( (2, 10) \). 2. **Graph Explanation**: - The graph displays a coordinate grid with both points \( A \) and \( B \) marked. - A line appears connecting the points \( A \) and \( B \) with a dotted rectangle outlining the vertical and horizontal segments between these points. 3. **Animating the Midpoint**: - Start by visualizing a right triangle formed from the x and y differences between the points. - Calculate the midpoint by using the midpoint formula: \[ \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \] - In this example, calculate: \[ x\text{-coordinate}: \frac{-6 + 2}{2} = -2 \] \[ y\text{-coordinate}: \frac{6 + 10}{2} = 8 \] 4. **Interactive Features**: - Click "Start over" to reset the graph or replot the midpoint. - Use the "Remove Rectangle" button to clear the rectangle. 5. **Submit Your Answer**: - Enter the calculated midpoint coordinates \( (-2, 8) \) in the provided fields. - Click "Submit Answer" to check your solution. ### Additional Information: This method helps students grasp the geometric interpretation of finding midpoints, reinforcing the understanding through a visual and interactive approach.
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