Exact Distance Geometry

Question

How do you find the exact distance between points L(7,-1) and M(-2,4)?

Answer 1

Distance formula can be applied here:

d = √[(y₂-y₁)²+(x₂-x₁)²]

d = √[(4-(-1))²+(-2-7)²]

d = √[(5)²+(-9)²]

d = √(25+81)

d = √106 units

Raymond's method is a more visual approach and uses the Pythagorean Theorem which is based on the distance formula.

Answer 2

square root of 106

use the Pythagorean Theorem

d^2 = 5^2 +9^2= 25+81= 106

L(7,-1) to M(-2,4)

plot them, connect them with a line segment

construct a right triangle

it's base is 7 --2 = 7+2 = 9

it's height is 4--1 = 4+1 = 5

the hypotentuse = sqr(9^2+5^2) =sqr(81+25)= sqr106

the hypotenuse = the distance between L and M

sqr106= 10.29563014... but that's not exact. the square root of 106 is an irrational number, which in decimal form is a non-repeating decimal that goes on forever.