Question

The coordinates of a triangle are (-1, 1) (3,0) (1, -4) , and . The coordinates of the translated triangle are (0,4) (4, 3) and (2, -1) . Find the translation vector.
A. (-1, -3)
B. (-1, -1)
C. (3, 3)
D. (1, 3)
E. (3, 1)
F. (-3, -1)

Answer 1

Answer:

D. $(1,3)$

Step-by-step explanation:

Given

$A = (-1,1)$

$B = (3,0)$

$C =(1,-4)$

$A' = (0,4)$

$B'=(4,3)$

$C = (2,-1)$

Required

The translation vector

Represent the translation vector with $(x,y)$

Taking points A and A' as points of reference, we have:

$A + (x,y) \to A'$ ---- The translation

This gives:

$(-1,1) + (x,y) \to (0,4)$

Collect like terms

$(x,y) \to (0,4) -(-1,1)$

Rewrite as:

$(x,y) \to (0 - -1,4-1)$

$(x,y) \to (1,3)$

Hence, the translation vector is $(1,3)$