Math Problem Statement

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.

Solution

To find the distance between Mary C's seat at (4,7)(-4, 7) and Betty C's seat at (2,5)(-2, 5), we use the distance formula for two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2):

d=(x2x1)2+(y2y1)2d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

Step-by-step calculation:

  1. Let (x1,y1)(x_1, y_1) be Mary's location (4,7)(-4, 7), and (x2,y2)(x_2, y_2) be Betty's location (2,5)(-2, 5).
  2. Calculate the differences in coordinates: (x2x1)=(2(4))=2(x_2 - x_1) = (-2 - (-4)) = 2 (y2y1)=(57)=2(y_2 - y_1) = (5 - 7) = -2
  3. Substitute into the distance formula: d=(2)2+(2)2=4+4=8d = \sqrt{(2)^2 + (-2)^2} = \sqrt{4 + 4} = \sqrt{8}
  4. Simplify: d=82.83d = \sqrt{8} \approx 2.83

Thus, the distance between Mary C's and Betty C's seats is approximately 2.832.83 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.

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Math Problem Analysis

Mathematical Concepts

Coordinate Geometry
Distance Formula
Cartesian Coordinates

Formulas

Distance formula: d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Theorems

Pythagorean Theorem (as basis for distance formula)

Suitable Grade Level

Grades 6-8