www.VirtualNerd.com

What Is the Distance Formula?

What is the distance formula?

Summary

  1. The lines labeled 'x' and 'y' are the x and y-axes
  2. We use subscripts '1' and '2' to distinguish between the two points
  3. The distance, or length, of the line segment is represented by the variable 'd'
  4. The symbol over the '(x2-x1)2+(y2-y1)2' is the square root sign
  5. The thin red line represents: 'x2-x1'
  6. The thin purple line represents: 'y2-y1'
  7. The square in the corner of the triangle means 90 degrees

Notes

    1. For this problem, think of distance as the length of a line segment connecting two points
    2. Those two points are called the 'endpoints' of a line segment
    1. There is a formula to find the distance, or length, of a line segment
    2. This distance is represented by the variable 'd'
    3. Each point has an x and y-coordinate
    4. We use subscripts 1 and 2 to distinguish between the two points
    5. The symbol over the '(x2-x1)2+(y2-y1)2' is the square root sign
    6. The exponent '2' means 'squared'
    1. Remember, 'length' here is the same as the distance
    2. The 'coordinates' are the ordered pairs we're finding the distance between
    3. So here the coordinates, or ordered pairs, would be (x1, y1) and (x2, y2)
    1. Make a horizontal line to represent the x-distance, shown on our diagram in red
    2. Add in a vertical line to represent the y-distance, shown on our diagram in purple
    3. These two lines intersect to form a right angle
    1. The x-coordinates are 'x1' and 'x2'
    2. We've represented 'x2-x1' with a red horizontal line on the graph
    1. The y-coordinates are 'y1' and 'y2'
    2. We've represented 'y2-y1' with a purple vertical line on the graph
    1. The longest side of a right triangle is called the hypotenuse
    2. 'd' is a variable representing 'distance'
    1. In a right triangle, one angle is 90 degrees and the longest side is the hypotenuse
    2. The exponent '2' means 'squared'
    3. Remember, the length of the red line is represented by 'x2-x1'
    4. Similarly, the length of the purple line is represented by 'y2-y1'
    5. 'd' is the hypotenuse since it's the longest side
    1. The symbol over all the variables is the square root sign
    2. The exponent '2' means 'squared'
    3. Taking the square root of anything that is already squared will get rid of the exponent '2'
    4. We keep the square root on the right so we can plug our red and purple sides right in!
    5. Taking the square root of 'd2' won't give you '±d' because you can't have a negative distance
    6. Since 'd' can only be positive, the other side of the equation will also be positive!