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

Answer:

See explanation

Step-by-step 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:

$A = (-1,1)$

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

$A' = (-2,1)$

$B = (3,3)$

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

$B'= (2,3)$

$C =(4,-2)$

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

$C'= (3,-2)$