△XYZ has vertices X(0,−2), Y(1,4), and Z(5,3). Which of the following represents the translation of △XYZ along vector <3,−4> and its reflection across the x-axis?
PLEASE HELP!!!
Answers:

X (0, −2) → X ′(3, −4) → X ″(−4, 3);
Y (1, 4) → Y ′(4, 0)→ Y ″(0, 4);
Z (5, 3)→ Z ′(8, 7)→ Z ″(−7, 8)

X (0, −2) → X ′(3, 2) → X ″(−2, 3);
Y (1, 4) → Y ′(4, 8) → Y ″(−8, 4);
Z (5, 3) → Z ′(8, 1) → Z ″(−8, 1)

X (0, −2) → X ′(3, −6) → X ″(3, 6);
Y (1, 4) → Y ′(4, 0) → Y ″(4, 0);
Z (5, 3)→ Z ′(8, −1)→ Z ″(8, 1)

X (0, −2) → X ′(0, 8) → X ″(0, −8);
Y (1, 4) → Y ′(3, −16) → Y ″(3, 16);
Z (5, 3) → Z ′(15, 12) → Z ″(15, −12)

X (0, −2) → X ′(3, −6) → X ″(3, 6);

Y (1, 4) → Y ′(4, 0) → Y ″(4, 0);

Z (5, 3)→ Z ′(8, −1)→ Z ″(8, 1)

Explanation:

use the rule for reflection: (x,y)→(x,−y)

X'(3,−6)→X''(3,6).

Y'(4,0)→Y''(4,0).

Z'(8,−1)→Z''(8,1).

X(0,−2)→X'(3,−6)→X''(3,6)

Y(1,4)→Y'(4,0)→Y''(4,0)

Z(5,3)→Z'(8,−1)→Z''(8,1)

X (0, −2) → X ′(3, −6) → X ″(3, 6);

Y (1, 4) → Y ′(4, 0) → Y ″(4, 0);

Z (5, 3)→ Z ′(8, −1)→ Z ″(8, 1)

Explanation:

Use the translation vector <3, −4>  to determine the rule for translation of the coordinates: (x, y) → (x + 3, y +(−4)).

Apply the rule to translate vertices X (0, −2), Y (1, 4), and Z (5, 3).

X (0, −2) → (0 + 3, −2 + (−4)) → X' (3, −6).

Y (1, 4) → (1 + 3, 4 + (−4)) → Y' (4, 0).

Z (5, 3) → (5 + 3, 3 + (−4)) → Z' (8, −1).

To apply the reflection across x-axis use the rule for reflection: (x, y) → (x, −y).

Apply the reflection rule to the vertices of △X'Y'Z'.

X ' (3, −6) → X '' (3, 6).

Y ' (4, 0) → Y '' (4, 0).

Z' (8, −1) → Z '' (8, 1).

Therefore,

X (0, −2) → X' (3, −6) → X'' (3, 6)

Y (1, 4) → Y' (4, 0) → Y'' (4, 0)

Z (5, 3) →Z' (8, −1) → Z'' (8, 1)

represents the translation of △XYZ along vector <3, −4>  and its reflection across the x-axis.

changes in factors like average income and preferences can cause an entire demand curve to shift right or left. this causes a higher or lower quantity to be demanded at a given price. demand curves relate the prices and quantities demanded assuming no other factors change. it is important for consumers to know this information, because it is crucial for them to know what they can afford and can't afford. i hope this .