Question

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

Answer 1

Answer: Correct answer is (x, y) → ( x − 3, y − 4); (5, −1)

Step-by-step explanation: Starting from point 8,3 we go down 4 on the y-axis (y-4)and stopping at -1 then we go left on the x-axis (x-3) stopping at 5.

So the new coordinate for the vertex C should read 5,-1.

Answer 2

After the translation , the coordinates of vertex C are ( 5 , -1 )

Further explanation

There are several types of transformations:

1. Translation
2. Reflection
3. Rotation
4. Dilation

Let us now tackle the problem!

This problem is about Translation.

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

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

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

A(-3 , 4) → A'(-3 + (-3) , 4 + (-4)) = A'(-6 , 0)

B(4 , -2) → B'(4 + (-3) , -2 + (-4)) = B'(1 , -6)

C(8 , 3) → C'(8 + (-3) , 3 + (-4)) = C'(5 , -1)

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

Conclusion:

After the translation , the coordinates of vertex C are ( 5 , -1 )

Learn more

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Answer details

Grade: High School

Subject: Mathematics

Chapter: Function

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