The class of math is mapped on a coordinate grade with the origin being the center of the point of the hall. Mary C is located at the point -4, seven and Betty C is located at -2, five how far is it from Mary seat to Betty seat.

To find the distance between Mary C's seat at \((-4, 7)\) and Betty C's seat at \((-2, 5)\), we use the distance formula for two points \((x_1, y_1)\) and \((x_2, y_2)\):

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

### Step-by-step calculation:
1. Let \((x_1, y_1)\) be Mary's location \((-4, 7)\), and \((x_2, y_2)\) be Betty's location \((-2, 5)\).
2. Calculate the differences in coordinates:
   \[
   (x_2 - x_1) = (-2 - (-4)) = 2
   \]
   \[
   (y_2 - y_1) = (5 - 7) = -2
   \]
3. Substitute into the distance formula:
   \[
   d = \sqrt{(2)^2 + (-2)^2} = \sqrt{4 + 4} = \sqrt{8}
   \]
4. Simplify:
   \[
   d = \sqrt{8} \approx 2.83
   \]

Thus, the distance between Mary C's and Betty C's seats is approximately \(2.83\) units.

Do you have any questions or want more details?

### Follow-up Questions:
1. How would you visualize this distance on a coordinate plane?
2. What are other methods to calculate the distance between points?
3. How does the distance formula change for three-dimensional space?
4. Can we calculate the slope of the line connecting these two points?
5. If the seats were aligned horizontally or vertically, how would the distance formula simplify?

**Tip:** The distance formula is an application of the Pythagorean Theorem and works for any two points on a plane.

Learn how to calculate the distance between two points (-4, 7) and (-2, 5) on a coordinate plane using the distance formula. This problem covers basic concepts in coordinate geometry, including Cartesian coordinates and the Pythagorean Theorem. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation