Question

Point A is located at (?5, 2) on a coordinate grid. Point A is translated 1 unit to the left and 5 units down to create point A'. Which measurement is closest to the distance between point A and point A' in units? A) 4.7 units B) 4.9 units C) 5.1 units D) 5.3 units

Answer 1

ANSWER

C) 5.1 units

EXPLANATION

The coordinates of A are (5,2).


If this point is translated 1 unit to the left and 5 units down to create point A'.

Then A' has coordinates

$A(5,2)\rightarrow \: A'(5-1,2-5)$


$A(5,2)\rightarrow \: A'(4, - 3)$



The distance between A and A' is calculated using the distance formula,

$|AA'| = \sqrt{ {(5 - 4)}^{2} + {(2 - - 3}^{2} }$


$|AA'| = \sqrt{ {(1)}^{2} + {(5)}^{2} }$


$|AA'| = \sqrt{ 26}$


$|AA'| = 5.099$

We round to the nearest tenth to obtain,

$|AA'| =5.1 \: units$


The measurement that is closed to the distance is 5.1 units