Question

Translate triangle a (-3,1) what do i write

Answer 1

Answer:

Rotate 180 degrees about the point (1.5, -0.5)

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Explanation:

Refer to the diagram below.

Let point A be located at (1,-1) which is the very top of the black triangle.

Shift three units to the left, and one unit up, and you should arrive at (-2,0)

Then rotate 180 degrees to land on (2,0) which I'll mark as point B.

In short, the point A(1,-1) moves to B(2,0)

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Through similar moves, the point C(1,-4) moves to D(2,3)

Next, find the equation of the line through points A and B. You should find that line AB has the equation y = x-1. Let me know if you need to see the steps on how to find the equation.

The equation for line CD is y = 7x-11

Upon solving this system of equations

$\begin{cases}y = x-1\\y = 7x-11\end{cases}$

you should find that x = 1.5 and y = -0.5

So that's how I got point E to be located at (1.5, -0.5)

Point E is the center of rotation when we combine the translation along with the original rotation.

In other words, to go from A to B as fast as possible, we rotate 180 degrees about point E. The same can be said when going from C to D.

So overall, rotating the original triangle A 180 degrees about (1.5, -0.5) will have it land on triangle C.