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.

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:

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:

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:

and

So, we have:

Hence, the coordinate of the new triangle will be:

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

-7

step-by-step explanation:

x^2 + 18x + 74 = (x + 9)^2 - 81 + 74

= (x + 9)^2 - 7.

so q = -7.