Use the Midpoint Formula repeatedly to find the three points that divide the line segment joining the given points into four equal parts. (а) (3, —2), (5, -1) (х, у) %3D 7 -7 2 4 (smallest x-value) (x, y) = 3 4, – (х, у) %3D 2 (largest x-value)

Calculus: Early Transcendentals
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Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Instructions**: Use the Midpoint Formula repeatedly to find the three points that divide the line segment joining the given points into four equal parts.

### (a) Between Points (3, -2) and (5, -1):

1. **First Midpoint**:
   \[
   (x, y) = \left(\frac{7}{2}, -\frac{7}{4}\right)
   \]
   *Note: This is the smallest x-value.*

2. **Second Midpoint**:
   \[
   (x, y) = \left(4, -\frac{3}{2}\right)
   \]

3. **Third Midpoint**:
   \[
   (x, y) = \left(\frac{9}{2}, -\frac{5}{4}\right)
   \]
   *Note: This is the largest x-value.*

### (b) Between Points (-3, -2) and (0, 0):

1. **First Midpoint**:
   \[
   (x, y) = \text{(smallest x-value)}
   \]

2. **Second Midpoint**:
   \[
   (x, y) = 
   \]

3. **Third Midpoint**:
   \[
   (x, y) = \text{(largest x-value)}
   \]

**Explanation**: The Midpoint Formula is used to find the point exactly halfway between two other points on a coordinate plane. The formula is given by:

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

This method is repeated to divide a straight line into equal segments. Here, it is applied to sequentially find three points that split the line segment into four equal parts.
Transcribed Image Text:**Instructions**: Use the Midpoint Formula repeatedly to find the three points that divide the line segment joining the given points into four equal parts. ### (a) Between Points (3, -2) and (5, -1): 1. **First Midpoint**: \[ (x, y) = \left(\frac{7}{2}, -\frac{7}{4}\right) \] *Note: This is the smallest x-value.* 2. **Second Midpoint**: \[ (x, y) = \left(4, -\frac{3}{2}\right) \] 3. **Third Midpoint**: \[ (x, y) = \left(\frac{9}{2}, -\frac{5}{4}\right) \] *Note: This is the largest x-value.* ### (b) Between Points (-3, -2) and (0, 0): 1. **First Midpoint**: \[ (x, y) = \text{(smallest x-value)} \] 2. **Second Midpoint**: \[ (x, y) = \] 3. **Third Midpoint**: \[ (x, y) = \text{(largest x-value)} \] **Explanation**: The Midpoint Formula is used to find the point exactly halfway between two other points on a coordinate plane. The formula is given by: \[ \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \] This method is repeated to divide a straight line into equal segments. Here, it is applied to sequentially find three points that split the line segment into four equal parts.
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