Question

In the coordinate plane, the point A (-4,1) is translated to the point A' (0,6). Under the same translation, the points B(0,3) and c (-1,-2) are translated to B' and C', respectively. What are the coordinates of B' and C'?

Answer 1

Answer:

Part 1) The rule of the translation is    (x,y) ------> (x+4,y+5)

Part 2) B'(4,8)

Part 3) C'(3,3)

Step-by-step explanation:

Part 1)

Find out the rule of the translation

we know that

The transformation of the point A to A' is equal to

A(-4,1) ------> A'(0,6)

so

The rule of the translation is equal to

(x,y) ------> (x+a,y+b)

(-4,1) ------> (-4+a,1+b)

Find the value of a

-4+a=0 -----> a=4

Find the value of b

1+b=6 -----> b=5

substitute the values of a and b

(x,y) ------> (x+4,y+5)

That means -----> The translation is 4 units at right and 5 units up

Part 2) Find out the coordinates of B'

Applying the rule of the translation

(x,y) ------> (x+4,y+5)

so

B(0,3) ------> B'(0+4,3+5)

B(0,3) ------> B'(4,8)

Part 3) Find out the coordinates of C'

Applying the rule of the translation

(x,y) ------> (x+4,y+5)

so

C(-1,-2) ------> C'(-1+4,-2+5)

C(-1,-2) ------> C'(3,3)