Triangle ABC has vertices at A(−3, 4), B(4, −2), C(8, 3). The triangle translates 4 units right and 3 units down. Which rule represents the translation? After the translation, what are the coordinates of vertex A?

A) (x, y) → ( x + 4, y + 3); (1, 7)

B) (x, y) → (x + 4, y − 3); A(1, 1)

C) (x, y) → (x − 4, y + 3); (−7, 1)

D) (x, y) → (x − 4, y − 3); A(1, −1)

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JeanaShupp JeanaShupp · Answer 1 · 2018-12-29T10:07:55+01:00

Answer: B) (x, y) → (x + 4, y − 3); A(1, 1)

Step-by-step explanation:

Given: Triangle ABC has vertices at A(−3, 4), B(4, −2), C(8, 3). The triangle translates 4 units right and 3 units down.

Now, 4 units right means adding 4 units to x coordinates of the figure, to get the x coordinate of the translated image.

Similarly , 3 units down means subtracting 3 units from the y coordinate of the figure, to get the x coordinate of the translated image.

Therefore, the translation rule becomes (x, y) → (x + 4, y − 3)

⇒A(-3,4)→(-3+4,4-3)=(1,1)

johanrusli johanrusli · Answer 2 · 2019-10-30T09:04:37+01:00

Rule represents the translation : (x, y) → (x + 4, y − 3) ( Option B )

The coordinates of vertex A are A(1, 1)

There are several types of transformations:

Let us now tackle the problem!

This problem is about Translation.

The triangle is translated 4 units right and 3 units down.

The rule that represents the translation will be [tex]\left[\begin{array}{ccc}4\\-3\end{array}\right][/tex]

Let's find the translation for every vertice of Triangle ABC:

( x , y ) → ( x + 4 , y - 3 )

A(-3 , 4) → A'(-3 + (4) , 4 + (-3)) = A'(1 , 1)

B(4 , -2) → B'(4 + (4) , -2 + (-3)) = B'(8 , -5)

C(8 , 3) → C'(8 + (4) , 3 + (-3)) = C'(12 , 0)

From the results above, we can illustrate the translation process as shown in the attached picture

After the translation , the coordinates of vertex A are ( 1 , 1 )

Grade: High School

Subject: Mathematics

Chapter: Function

Keywords: Function , Trigonometric , Linear , Quadratic , Translation , Reflection , Rotation , Dilation , Graph , Vertex , Vertices , Triangle