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The coordinates of the image of triangle are transformation are X = (1,3), Y = (5,-3) and Z = (-1, -7)
<h3>How to determine the transformation?</h3>From the figure, the coordinates of the triangle are:
A = (-1, -1)
B = (1, 2)
C = (-2,4)
The transformation rule is given as:
This means that, we start by dilating the triangle by a scale factor of 2.
So, we have:
A' = (-2, -2)
B' = (2, 4)
C' = (-4,8)
Next, we rotate the triangle across the x-axis
So, we have:
A'' = (-2, 2)
B'' = (2, -4)
C'' = (-4,-8)
Lastly, we translate the triangle by (x + 3,y + 1) to get the triangle XYZ
So, we have:
X = (1,3)
Y = (5,-3)
Z = (-1, -7)
See attachment for the image of the transformation
Read more about transformation at:
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Check the picture below.
based on the equation, if we set y = 0, we'd end up with 0 = 0.5(x-3)(x-k).
and that will give us two x-intercepts, at x = 3 and x = k.
since the triangle is made by the x-intercepts and y-intercepts, then the parabola most likely has another x-intercept on the negative side of the x-axis, as you see in the picture, so chances are "k" is a negative value.
now, notice the picture, those intercepts make a triangle with a base = 3 + k, and height = y, where "y" is on the negative side.
let's find the y-intercept by setting x = 0 now,
now, we can plug those values on A = (1/2)bh,
