Math Problem Statement

find the distance btween P(1,-3) and Q(3,-4)

Solution

To find the distance between points P(1,3)P(1, -3) and Q(3,4)Q(3, -4), we use the distance formula:

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

Given:

  • P(x1,y1)=(1,3)P(x_1, y_1) = (1, -3)
  • Q(x2,y2)=(3,4)Q(x_2, y_2) = (3, -4)

Substitute the values:

d=(31)2+(4+3)2d = \sqrt{(3 - 1)^2 + (-4 + 3)^2}

=(2)2+(1)2= \sqrt{(2)^2 + (-1)^2}

=4+1= \sqrt{4 + 1}

=5= \sqrt{5}

So, the distance between points PP and QQ is 5\sqrt{5}.

Would you like a detailed explanation of each step?


Related Questions:

  1. How do you find the midpoint between two points?
  2. What is the distance between the points (2,3)(2, 3) and (1,2)(-1, -2)?
  3. How can you find the distance between points on a 3D plane?
  4. Can the distance formula be derived from the Pythagorean Theorem?
  5. What is the significance of the distance formula in coordinate geometry?

Tip: For easier calculations, keep square roots in radical form unless you need a decimal approximation.

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Math Problem Analysis

Mathematical Concepts

Coordinate Geometry
Distance Calculation

Formulas

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

Theorems

Pythagorean Theorem

Suitable Grade Level

Grades 7-9