Question

What is the distance between ( 8 , − 3 ) (8,−3)left parenthesis, 8, comma, minus, 3, right parenthesis and ( 4 , − 7 ) (4,−7)left parenthesis, 4, comma, minus, 7, right parenthesis?

Answer 1

Given Information:

Point 1 =  (8, −3)

Point 2 =  (4, −7)

Required Information:

Distance between points = d = ?

Answer:

Distance between points = d = √32 = 5.657

Step-by-step explanation:

We are given two points,

(x₁, y₁) = (8, −3)

(x₂, y₂) = (4, −7)

We are asked to find the distance between these two points.

The distance is given by

$d = \sqrt{(x_2 - x_1)^2 +(y_2 - y_1)^2 }$

Substitute the given coordinates into above equation

$d = \sqrt{(x_2 - x_1)^2 +(y_2 - y_1)^2 } \\\\d = \sqrt{(4 - 8)^2 +(-7 - (-3))^2 } \\\\d = \sqrt{(-4)^2 +(-7 +3)^2 } \\\\d = \sqrt{(-4)^2 +(-4)^2 } \\\\d = \sqrt{16 +16 } \\\\d = \sqrt{32} \\\\d = 5.657$

Therefore, the distance between (8, −3) and (4, −7) is 5.657 units.