Question

First, the triangle is dilated by a scale factor of 1/3 about the origin. Then the triangle is reflected over the x-axis. Finally, the triangle is translated left 3 units and up 2 units.

Answer 1

Answer:

$(\frac{1}{3}x - 3,-\frac{1}{3}y+2)$

Both triangles will be similar

Step-by-step explanation:

See comment for complete question.

Given

Let the coordinates of the triangle be T(x,y)

First transformation: Dilation by 1/3

The new points will be:

$T' = \frac{1}{3}(x,y)$

$T' = (\frac{1}{3}x,\frac{1}{3}y)$

Second: Reflection over the x-axis

When a point (x,y) is reflected over the x-axis, the new point is (x,-y).

So, we have:

$T'' = (\frac{1}{3}x,-\frac{1}{3}y)$

Third: Translation 3 units left and 2 units up.

When a point (x,y) is translated b units left and h units up, the new point is (x - b,y+h).

In this case:

$b = 3$ and $h = 2$

So, we have:

$T''' = (\frac{1}{3}x - 3,-\frac{1}{3}y+2)$

Hence, the coordinate of the new triangle will be: $(\frac{1}{3}x - 3,-\frac{1}{3}y+2)$

Additionally, both triangles will be similar because all the transformation done are rigid transformations i.e. Dilation, Reflection and Translation