Math Problem Statement

What is the distance between (5, 9) and (-7, -7)?

Solution

To solve this problem, we can use the distance formula:

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

where (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) are the two points.

For the points (5,9)(5, 9) and (7,7)(-7, -7), we can substitute into the formula:

  • x1=5x_1 = 5, y1=9y_1 = 9
  • x2=7x_2 = -7, y2=7y_2 = -7

Now, let's calculate the distance:

d=(75)2+(79)2=(12)2+(16)2=144+256=400=20d = \sqrt{{(-7 - 5)^2 + (-7 - 9)^2}} = \sqrt{{(-12)^2 + (-16)^2}} = \sqrt{{144 + 256}} = \sqrt{{400}} = 20

So, the distance between the two points is 20 units.

Would you like a detailed breakdown or have any questions?

Here are 5 related questions for practice:

  1. What is the distance between (3,4)(3, 4) and (7,1)(7, 1)?
  2. If two points are (2,8)(2, 8) and (10,6)(10, -6), what is their distance?
  3. How does the distance formula change in 3D space?
  4. What is the midpoint between (5,9)(5, 9) and (7,7)(-7, -7)?
  5. Can you calculate the distance between (3,5)(-3, 5) and (6,2)(6, 2)?

Tip: Always double-check the signs when substituting values into the distance formula!

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Math Problem Analysis

Mathematical Concepts

Geometry
Distance between two points
Coordinate geometry

Formulas

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

Theorems

Pythagorean theorem

Suitable Grade Level

Grades 8-10