Question

The point A(-6,-5) is translated using T: (x,y) - (x + 4, y + 6).

Answer 1

Answer:

$d=\sqrt{52}$

$d \approx 7.211$

(If you want the simplified form of the exact distance (line 1):

$\sqrt{52}=\sqrt{4}\sqrt{13}=2\sqrt{13}$.

Step-by-step explanation:

A is at (-6,-5).

We are given A' can be found by inserting A s point into:

T(x,y)   ->(x+4,y+6)

T(A)     ->(-6+4,-5+6)

T(-6,-5)->(  -2  ,   1   ).

So we need to find the distance between A and A'; that is find the distance between (-6,-5) and (-2,1).

The distance formula is

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

So we need to find the change in x; the difference between the x's.  I like to obtained the positive difference for x and y when doing distance formula.  It absolutely does matter which way you do your x's and which way you do your y's as long as you subtract them.  The reason is because of the square.

The x-difference is= (-2)  -   (-6)  = -2  + 6=4.

The y-difference is= (1)   -    (-5)  =   1  +  5=6.

Back to the distance formula:

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

$d=\sqrt{(4)^2+(6)^2}$

$d=\sqrt{16+36}$

$d=\sqrt{52}$

$d \approx 7.211$