Math Problem Statement

Calculate the distance between the points M(-1, 4) and N(4, -1) in the coordinate plane. Round your answer to the nearest hundredth.

Solution

The problem asks to calculate the distance between two points M(1,4)M(-1,4) and N(4,1)N(4,-1) in the coordinate plane, rounding to the nearest hundredth. We will use the distance formula for two points in a plane, which is:

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

Where:

  • M(x1,y1)=(1,4)M(x_1, y_1) = (-1, 4)
  • N(x2,y2)=(4,1)N(x_2, y_2) = (4, -1)

Let me calculate the distance.The distance between the points M(1,4)M(-1, 4) and N(4,1)N(4, -1) is approximately 7.077.07, rounded to the nearest hundredth.

Do you want more details or have any other questions?

Here are 5 related questions for practice:

  1. How would the distance formula change if the points were three-dimensional?
  2. What is the midpoint between the points M(1,4)M(-1, 4) and N(4,1)N(4, -1)?
  3. How do you derive the distance formula from the Pythagorean theorem?
  4. If you shift both points up by 3 units, what will the new distance be?
  5. How can you calculate the length of a diagonal in a rectangle using the distance formula?

Tip: Always square the differences in the coordinates before summing them in the distance formula to avoid negative values.

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Math Problem Analysis

Mathematical Concepts

Geometry
Coordinate Plane
Distance Formula

Formulas

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

Theorems

Pythagorean Theorem

Suitable Grade Level

Grades 8-10