Find the distance between the given points.

a. (1, 1) and (5, 5)

b. (1, 3/2) and (-7,-5/2)

To find the distance between two points \((x_1, y_1)\) and \((x_2, y_2)\) in a plane, we use the distance formula:

\[
\text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

Let's apply this formula to both pairs of points:

### a. Points \((1, 1)\) and \((5, 5)\)

\[
\text{Distance} = \sqrt{(5 - 1)^2 + (5 - 1)^2} = \sqrt{(4)^2 + (4)^2} = \sqrt{16 + 16} = \sqrt{32} = 4\sqrt{2}
\]

### b. Points \((1, \frac{3}{2})\) and \((-7, -\frac{5}{2})\)

\[
\text{Distance} = \sqrt{\left(-7 - 1\right)^2 + \left(-\frac{5}{2} - \frac{3}{2}\right)^2} = \sqrt{(-8)^2 + \left(-\frac{8}{2}\right)^2} = \sqrt{64 + 16} = \sqrt{80} = 4\sqrt{5}
\]

### Final Answers:
- **a.** The distance between \((1, 1)\) and \((5, 5)\) is \(4\sqrt{2}\).
- **b.** The distance between \((1, \frac{3}{2})\) and \((-7, -\frac{5}{2})\) is \(4\sqrt{5}\).

Would you like further details or have any questions?

### Related Questions:
1. How would the distance formula change in three-dimensional space?
2. What is the distance between points \((0, 0)\) and \((8, 6)\)?
3. How can the distance formula be derived from the Pythagorean theorem?
4. What is the significance of the square root in the distance formula?
5. How do you find the midpoint between two points on a plane?

### Tip:
Always double-check your subtraction steps when applying the distance formula to avoid errors in calculation.

Learn how to calculate the distance between two points (1, 1) and (5, 5) using the distance formula. Also, find the distance between points (1, 3/2) and (-7, -5/2) with detailed step-by-step solutions. Suitable for high school students studying coordinate geometry.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation