https://file.aiquickdraw.com/mathbot/file/17254089588658z39upaq.jpg

I see that you've uploaded a photo of your math assignment. Let's analyze the content step by step.

### Problem Description:
You are asked to graph a right triangle with the points \((-5, 8)\) and \((-9, 4)\), forming the hypotenuse. Then, using the sides, you need to find the distance between these points.

### What the image shows:
1. **The Coordinate Points**: \((-5, 8)\) and \((-9, 4)\).
2. **Graph**: The points \((-5, 8)\) and \((-9, 4)\) are plotted on a graph. 
3. **Distance Formula**: The formula for distance between two points is used: 
   \[
   d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
   \]
   where \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of the points.
4. **Calculations**: 
   \[
   d = \sqrt{(-9 + 5)^2 + (4 - 8)^2} = \sqrt{(-4)^2 + (-4)^2} = \sqrt{16 + 16} = \sqrt{32} \approx 5.7
   \]
   The distance calculated is approximately 5.7 units.

### Interpretation:
- The points given form the hypotenuse of a right triangle. You correctly applied the distance formula to find the length of the hypotenuse.
- The intermediate steps, including the subtraction of the coordinates, squaring, adding, and finally taking the square root, are all correctly executed.

### Would you like more details or have any questions about this problem?

Here are five related questions for further exploration:
1. How do you determine the lengths of the other two sides of the right triangle?
2. What would the slope of the hypotenuse be, and how could you find it?
3. How can the midpoint of the hypotenuse be calculated?
4. What is the area of the right triangle formed by these points?
5. If one point were shifted along the x-axis, how would the distance between the points change?

**Tip**: Always double-check your calculations when working with square roots, especially if you need to provide an exact answer instead of an approximation.

Graph a right triangle with the points (-5, 8) and (-9, 4) forming the hypotenuse. Find the distance between these points using the sides.

This problem involves graphing a right triangle with points (-5, 8) and (-9, 4) on a coordinate plane. The solution includes using the distance formula to find the hypotenuse, calculated as approximately 5.7 units. Suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation