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

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Answer 1 · 2015-12-07T15:51:13

$d~~9.49$ to 2 decimal places

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

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
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More accurately

$d=sqrt(9xx10)$

$d=sqrt(3^2xx10)$

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

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