Math Problem Statement

distance formula (-5,7)(7,0)

Solution

The distance formula is used to find the distance between two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) in a coordinate plane. The formula is:

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

Given the points (5,7)(-5, 7) and (7,0)(7, 0):

  1. x1=5x_1 = -5, y1=7y_1 = 7
  2. x2=7x_2 = 7, y2=0y_2 = 0

Now, substitute these values into the formula:

d=(7(5))2+(07)2d = \sqrt{(7 - (-5))^2 + (0 - 7)^2}

Simplify inside the parentheses:

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

d=122+(7)2d = \sqrt{12^2 + (-7)^2}

d=144+49d = \sqrt{144 + 49}

d=193d = \sqrt{193}

Therefore, the distance between the points (5,7)(-5, 7) and (7,0)(7, 0) is:

d=19313.89d = \sqrt{193} \approx 13.89

Would you like more details or have any questions?

Here are some related questions:

  1. What is the midpoint between two points (5,7)(-5, 7) and (7,0)(7, 0)?
  2. How can the distance formula be used in 3D space?
  3. What is the equation of a line passing through the points (5,7)(-5, 7) and (7,0)(7, 0)?
  4. Can the distance formula be derived from the Pythagorean theorem?
  5. What is the slope of the line between (5,7)(-5, 7) and (7,0)(7, 0)?

Tip: Remember that the distance formula is essentially an application of the Pythagorean theorem!

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Math Problem Analysis

Mathematical Concepts

Geometry
Coordinate Geometry
Distance Between Points

Formulas

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

Theorems

Pythagorean Theorem

Suitable Grade Level

Grades 8-10