A point X has coordinates (-1, -8). The point is reflected across the y-axis to form X' X' is translated over 4 to the right and up 6 to form X". What are the coordinates of X' and X" ?

X' ( 1 , -8 )

X'' ( 5,-2 )

Step-by-step explanation:

Given:-

- Point X : ( -1 , -8 )

Find:-

The point is reflected across the y-axis to form X', X' ?

X' is translated over 4 to the right and up 6 to form X", X''?

Solution:-

- We will look at each transformation step-by-step.

- The first transformation is the reflection of point X ( -1 , -8 ) across y-axis. That is the reflected point X' will have the same y coordinate. The distance in units of point X from y-axis is reflected across with the same units on the opposite side. Hence, the transformed X' would be:

                               X ( -1 , -8 )

                               x = -1 , y = -8

                               x' = 1 , y' = -8

                               X' ( 1 , -8 )

- Now the reflected X' is shifted 4 units right and 6 units up. That is there is an increase in x' by 4 units and increase in y' by 6 units to get X'':

                              X' ( 1 , -8 )

                              x' = 1 , y' = -8

                              x'' = 1 + 4 = 5 , y'' = -8 + 6 = -2

                              X'' ( 5,-2 )

To find the solutions to this equation, we can apply the quadratic formula. This quadratic formula solves equations of the form ax^2 + bx + c = 0
                                           x = [ -b ± √(b^2 - 4ac) ] / (2a)
                                           x = [ -8 ± √((8)^2 - 4(2)(3)) ] / ( 2(2) )
                                           x = [-8 ± √(64 - (24) ) ] / ( 4 )
                                           x = [-8 ± √(40) ] / ( 4)
                                           x = [-8 ± 2*sqrt(10) ] / ( 4 )
                                           x = -2 ± sqrt(10)/2
The answers are -2 + sqrt(10)/2 and -2 - sqrt(10)/2.