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

D.
`(1,3)`

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)`