Question

I NEED HELP

THERE ARE TWO OTHER QUESTIONS AS WELL

Answer 1

Please find attached the drawing of ABCD, A'B'C'D', and A''B''C''D'', created with MS Excel

Explanation:

The given composition of transformation is
`r_(y-axis) \ \circ \ r_(x = - 4)`

The transformation on the right,
`r_(x = - 4)`, is carried out first as follows;

The point A with coordinate (-7, 7) reflected across the line x = -4, gives;

A(-7, 7)
`r_(x = - 4)` → A'(-1, 7)

Similarly, we have;

B(-5, 7)
`r_(x = - 4)` → B'(-3, 7)

C(-5, 1)
`r_(x = - 4)` → C'(-3, 1)

D(-7, 1)
`r_(x = - 4)` → D'(-1, 1)

Therefore, the image of the given rectangle after reflection across the lie, x = -4, is A'(-1, 7), B'(-3, 7), C'(-3, 1), and D'(-1, 1)

The second transformation,
`r_(y-axis)`, is found as follows;

(x, y)
`r_(y-axis)` → (x, -y)

Therefore, we have;

A'(-1, 7)
`r_(y-axis)` → A''(-1, -7)

B'(-3, 7)
`r_(y-axis)` → B''(-3, -7)

C'(-3, 1)
`r_(y-axis)` → C''(-3, -1)

D'(-1, 1)
`r_(y-axis)` → D''(-1, -1)

The points ABCD, A'B'C'D', and A''B''C''D'' are plotted on MS Excel and the points joined with straight lines to form the drawing of the triangles as shown in the attached figure.