Question

a. Rotate the letter W 180° around the origin. Then translate the image up 4 units. Draw the final image. What new letter did you form? b. Is the new letter congruent to the original letter? Explain.

Answer 1

ANSWER and EXPLANATION

We have letter W on the graph.

The cordinates of its vertices are:

(0, 4), (1, 0), (2, 2), (3, 0), (4, 4)

Now, on a cartesian plane, (x - y plane), we have 4 quadrants. The letter is on the first quadrant.

Because it rotates 180 degrees around the origin, it means that it mmoves by 2 quadrants:

So, it moves from quadrant 1 to quadrant 4.

The new cordinates become:

(0, -4), (-1, 0), (-2, -2), (-3, 0), (-4, -4)

Then it is translated 4 units up, so we add 4 units to each of the y values (Remember that cordinates are written as (x, y)):

(0, 0), (-1, 4), (-2, 2), (-3, 4), (-4, 0)

Now, plot those:

a) It forms the letter M.

b) For one shape to be congruent to another, it means that they have the same size. So, yes, the M is congruent to the W.