Question

The vertices of figure BCDE have coordinates B(4, 4) , C(−4, 4), D(−4, −4) , and E(4, −4) . The vertices of figure B'C'D'E' have coordinates B'(2, 6) , C′(−6, 6), D′(−6, −2) , and E′(2, −2) .
Which transformation of ​ figure BCDE ​ produces ​ figure B'C'D'E' ​ ?


a translation 2 units left and 2 units up

a translation 2 units right and 2 units down

a reflection across the x-axis

a reflection across the y-axis

Answer 1

Answer:

1. a translation 2 units left and 2 units up

Step-by-step explanation:

We have the figure BCDE with co-ordinates,

B = (4,4), C = (-4,4), D = (-4,-4) and E = (4,-4).

It is given that, the figure BCDE is transformed to make new figure B'C'D'E' with co-ordinates,

B' = (2,6), C' = (-6,6), D' = (-6,-2) and E' = (2,-2).

Thus, we see that,

B = (4,4) = (4,4) + (-2,2) = (2,6)

C = (-4,4) = (-4,4) + (-2,2) = (-6,6)

D = (-4,-4) = (-4,-4) + (-2,2) = (-6,-2)

E = (4,-4) = (4,-4) + (-2,2) = (2,-2)

So, we get that the co-ordinates are changing by the addition of the co-ordinate (-2,2).

This means that the function is translated 2 units to the left and 2 units upwards.

Hence, transformation applied is 'a translation of 2 units to the left and 2 units upward'.

Answer 2

a translation 2 units left and 2 units up