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Rectangle [tex]\(ABCD\)[/tex] has vertex coordinates [tex]\(A(1, -2), B(4, -2), C(4, -4)\)[/tex], and [tex]\(D(1, -4)\)[/tex]. It is translated 1 unit to the left and 3 units up. What are the coordinates of [tex]\(B'\)[/tex]?

A. [tex]\((1, -1)\)[/tex]

B. [tex]\((3, 1)\)[/tex]

C. [tex]\((7, -3)\)[/tex]

D. [tex]\((5, -5)\)[/tex]



Answer :

GinnyAnswer
To determine the new coordinates of [tex]\( B' \)[/tex] after translating the rectangle [tex]\( ABCD \)[/tex], we need to carefully follow each translation step for vertex [tex]\( B \)[/tex].

1. Identify the coordinates of vertex [tex]\( B \)[/tex]:
Vertex [tex]\( B \)[/tex] has coordinates [tex]\( B(4, -2) \)[/tex].

2. Translate 1 unit to the left:
Translating a point to the left decreases its x-coordinate by the number of units specified.
[tex]\[ x' = 4 - 1 = 3 \][/tex]

3. Translate 3 units up:
Translating a point upwards increases its y-coordinate by the number of units specified.
[tex]\[ y' = -2 + 3 = 1 \][/tex]

4. Combine the new x and y coordinates:
After the translations, the new coordinates of [tex]\( B' \)[/tex] are:
[tex]\[ B' = (3, 1) \][/tex]

Thus, the coordinates of [tex]\( B' \)[/tex] are [tex]\((3, 1)\)[/tex].

The correct answer is:
B. [tex]\((3, 1)\)[/tex]

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