Question

11. The coordinates of AABC are A(-1,1), B(3,3),

and C(4, -2). Find the coordinates of points A', B',
and C' under the translations that take
a. P(0,0) to Q(1,3)
b. P(0, -1) to Q(4,-2)
c. P(-1,-2) to Q(-2,2)

Answer 1

See explanation

Explanation:

Given

`A = (-1,1)`

`B = (3,3)`

`C =(4,-2)`

Solving (a):
`P(0,0) \to Q(1,3)`

This means that:

`(x,y) \to (x+1,y+2)`

So, we have:

`A = (-1,1)`

`A' = (-1 + 1,1+2)`

`A' = (0,3)`

`B = (3,3)`

`B'= (3 + 1,3+2)`

`B'= (4,5)`

`C =(4,-2)`

`C' = (4+1,-2+1)`

`C' = (5,-1)`

Solving (b):
`P(0,-1) \to Q(4,-2)`

This means that:

`(x,y) \to (x+4,y-1)`

So, we have:

`A = (-1,1)`

`A' = (-1+4,1-1)`

`A' = (3,0)`

`B = (3,3)`

`B'= (3+4,3-1)`

`B'= (7,2)`

`C =(4,-2)`

`C' = (4+4,-2-1)`

`C' = (8,-3)`

Solving (c):
`P(-1,-2) \to Q(-2,-2)`

This means that:

`(x,y) \to (x-1,y)`

So, we have:

`A = (-1,1)`

`A' = (-1-1,1)`

`A' = (-2,1)`

`B = (3,3)`

`B'= (3-1,3)`

`B'= (2,3)`

`C =(4,-2)`

`C'= (4-1,-2)`

`C'= (3,-2)`