How do you find the distance between points (-7,8), (3,10)?

Question

Eva Abramson · Accepted Answer

undefined To find the distance between two points, you can use the distance formula. The distance formula is derived from the Pythagorean theorem and is given by:

d = √((x2 - x1)^2 + (y2 - y1)^2)

Using the given points (-7,8) and (3,10), we can substitute the values into the formula:

d = √((3 - (-7))^2 + (10 - 8)^2)

Simplifying further:

d = √((3 + 7)^2 + (10 - 8)^2)

d = √(10^2 + 2^2)

d = √(100 + 4)

d = √104

Therefore, the distance between the points (-7,8) and (3,10) is √104.

Eva Abramson · Answer

See a solution process below:

The formula for calculating the distance between two points is: #d = sqrt((color(red)(x_2) - color(blue)(x_1))^2 + (color(red)(y_2) - color(blue)(y_1))^2)# Substituting the values from the points in the problem gives: #d = sqrt((color(red)(3) - color(blue)(-7))^2 + (color(red)(10) - color(blue)(8))^2)# #d = sqrt((color(red)(3) + color(blue)(7))^2 + (color(red)(10) - color(blue)(8))^2)# #d = sqrt(10^2 + 2^2)# #d = sqrt(100 + 4)# #d = sqrt(104)# #d = sqrt(4 * 26)# #d = sqrt(4)sqrt(26)# #d = 2sqrt(26)# Or #d = 2 * 5.099# #d = 10.198# rounded to the nearest thousandth.