Question

Find the distance between the points (0, –1) and (3, –3).

A. 25
B. 5
C. √13
D. 13

Answer 1

To answer this, you basically use Pythagoras' Theroem, but instead of:

`c = \sqrt{a^(2) + b^(2)}`

it will be :

`distance = \sqrt{(y - y1)^(2) + (x - x1)^(2)  }`

So you are finding the squareroot of the (difference in y coordinates)² plus (difference in x coordinates) ²:

x is the x-coordinate of (0, -1) (so x = 0)

y is the y-coordinte of (0, -1) ( so y = -1)

x1 is the x coordinate of (3, -3) ( so x1 = 3)

y1 is the y coordinate of (3, -3) (so y1 = -3)

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Now, lets find the distance between the two points, by substituting all of this values into the equation at the top:

`distance = \sqrt{(y - y1)^(2) + (x - x1)^(2)  }` (substitute in values)

`distance = \sqrt{( 0 -3)^(2) + (-1 - -3)^(2) }` (simplify: note -1 - - 3 = -1 + 3)

`distance = \sqrt{( -3)^(2) + (-1 +3)^(2) }` (simplify)

`distance = \sqrt{( -3)^(2) + (2)^(2) }` (now square the numbers)

`distance = √(9 + 4 )` (simplify)

`distance = √(13 )`

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Answer:

C.
`√(13)`

Answer 2

C. √13

Explanation:

The distance between two points is given by

d =sqrt( (x2-x1)^2 + (y2-y1)^2)

= sqrt( (3-0)^2 + (-3--1)^2)

= sqrt( 3^2 + (-3+1)^2)

= sqrt( 9+(-2)^2)

= sqrt( 9+4)

= sqrt(13)