Question

∆ has the coordinates (3, 1), (5, 2), (4, 3). ∆´´´ has coordinates (-1, 2), (1, 3) and (0, 4). Which choice describes the translation of ∆ to ∆´´? A +4 units in the direction of x and -1 units in the direction of y B -4 units in the direction of x and +1 units in the direction of y C +4 units in the direction of x and +1 units in the direction of y D -4 units in the direction of x and -1 units in the direction of y

Answer 1

B -4 units in the direction of x and +1 units in the direction of y

Explanation:

Given

`A = (3, 1), (5, 2), (4, 3)`

`A^(-1)= (-1, 2), (1, 3) (0, 4)`

Required

Determine the translation from A to A-1

Take (3,1) from A and (-1,2) fro A-1 as points of reference,

For translation to occur, we make use of:

`(3 + x,1+y) = (-1,2)`

By comparison:

`3 + x = -1` and
`1 + y = 2`

Solve for x and y

`3 + x = -1`

`x = -1-3`

`x = -4`

`1 + y = 2`

`y = 2 - 1`

`y=1`

(B) is correct.