Math Problem Statement

M(-5,9) and n(-2,7)

Solution

To understand what you are asking, I'll assume you want to find the distance between the points M(-5, 9) and N(-2, 7). The distance between two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) in a plane can be calculated using the distance formula:

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

Given:

  • M(5,9)M(-5, 9) where x1=5x_1 = -5 and y1=9y_1 = 9
  • N(2,7)N(-2, 7) where x2=2x_2 = -2 and y2=7y_2 = 7

Plugging these values into the formula:

d=(2(5))2+(79)2d = \sqrt{(-2 - (-5))^2 + (7 - 9)^2}

Let's compute this.The distance between points M(-5, 9) and N(-2, 7) is approximately 3.61 units.

Would you like more details on this, or do you have any questions?

Here are 5 related questions you might find interesting:

  1. How do you calculate the midpoint between two points?
  2. What is the slope of the line passing through points M and N?
  3. How do you determine if two points lie on the same vertical or horizontal line?
  4. Can you derive the equation of the line passing through points M and N?
  5. How do you use the distance formula in three-dimensional space?

Tip: For solving geometric problems, always plot the points on a coordinate plane to visualize the scenario better.

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Math Problem Analysis

Mathematical Concepts

Coordinate Geometry
Distance Formula

Formulas

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

Theorems

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Suitable Grade Level

Grades 7-9