What is the distance between (2, 5) (2,5) and (–7, 8) ?

1 Answer
Dec 7, 2015

d~~9.49 to 2 decimal places

d= 3sqrt(10)color(white)(....)color(blue)("exactly!")

Explanation:

Tony B

Let the distance between be d

Let (x_1,y_1) -> (2,5)
Let (x_2,y_2)-> (-7,8)

color(brown)("Using Pythagoras:")

d^2 = ("difference in x")^2 +("difference in y")^2

d^2 = (x_2 - x_1)^2+(y_2 -y_1)^2

d^2 = (-7-2)^2+(8-5)^2

d^2 = (-9)^2+(3)^2

d^2= 81+9 = 90

d=sqrt(90)

d~~9.49 to 2 decimal places
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

More accurately

d=sqrt(9xx10)

d=sqrt(3^2xx10)

d= 3sqrt(10)color(white)(....)color(blue)("exactly!")