Please help me with these two geometry tasks...I'm really struggling

Question

The first one is -

Given triangle ABC with vertices (-8,2), (-2,2), and (-2, 8), create triangle DEF in quadrant one that uses a translation, rotation, and reflection (in any order) to map triangle DEF to triangle ABC. 

And the second task - On your graph paper, plot points A(-5, -2), B(-3, -2), and D(-5, -4). Mark point C to make a square in the third quadrant. Name the coordinate rule that will rotate the rectangle to the fourth quadrant, with vertex C’ at point (4, -3).

Please help me solve these and understand them in the process..I already solved them on my own but I'm not sure I did it right. I would be very grateful for your guidance.

Answer 1

First:

Do the problem "backwards". Start with ABC then

a) translate 9 or more units to the right, or

b) reflect over the y-axis, or

c) rotate about the origin.

Then label result DEF.

Second:

Draw and label C = (-3, -4)

Reflect over the y-axis.

Geometry is visual. Everything shown be drawn and labeled!

Answer 2

The following is only one of infinite ways of doing this.

It is easier to start from the target (ABC) and work backwards, one transformation at a time, as suggested by the other tutor.

Step 1:Translate right one unit and down two units.

D = (1,4) --> D' = (2,2)

E = (1,10) --> E' = (2,8)

F = (7,4) --> F' = (8,2)

Step 2: Rotate 180 degrees.

D' --> D'' = (-8,-2)

E' --> E'' = (-2,-2)

F' --> F'" = (-2,-8)

Step 3: Reflection across the x-axis.

D'' --> A = (-8,2)

E'' --> B = (-2,2)

F'" --> C = (-2,8)

☆☆☆☆☆☆☆☆☆☆

The second problem asks for a rotation. A 90 degree counter-clockwise rotation will do it.

C = ( -3 , -4 ) --> C' = ( -4, 3 )

90 degree CCW rotation switches the X and Y and changes the sign of the new Y.