∆ 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

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MrRoyal MrRoyal · Answer 1 · 2021-02-23T02:47:37+01:00

Answer:

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

Step-by-step explanation:

Given

[tex]A = (3, 1), (5, 2), (4, 3)[/tex]

[tex]A^{-1}= (-1, 2), (1, 3) (0, 4)[/tex]

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:

[tex](3 + x,1+y) = (-1,2)[/tex]

By comparison:

[tex]3 + x = -1[/tex] and [tex]1 + y = 2[/tex]

Solve for x and y

[tex]3 + x = -1[/tex]

[tex]x = -1-3[/tex]

[tex]x = -4[/tex]

[tex]1 + y = 2[/tex]

[tex]y = 2 - 1[/tex]

[tex]y=1[/tex]

(B) is correct.