Question

a triangle with vertices at (1,2), (3,2), and (2,4) is reflected over the y - axis and then rotated 90 degrees clockwise. what are the new coordinates of the vertex (1,2)?
a. (-1,-2)
b. (-2,1)
c. (2,1)
d. (-2,-1)

if a rectangle is translated 5 units left and 3 units down, what will happen to the coordinates of the vertices?
a. the x - coordinates increase by 5, and the y - coordinates decrease by 3.
b. the x - coordinates decrease by 5, and the y - coordinates decrease by 3.
c. the x - coordinates increase by 5, and the y - coordinates increase by 3.
d. the x - coordinates decrease by 5, and the y - coordinates increase by 3.

Explanation:

Step1: Reflect over y - axis

When reflecting a point $(x,y)$ over the y - axis, the transformation rule is $(-x,y)$. For the point $(1,2)$, after reflection over the y - axis, it becomes $(-1,2)$.

Step2: Rotate 90 degrees clockwise

The rule for a 90 - degree clockwise rotation of a point $(x,y)$ is $(y,-x)$. For the point $(-1,2)$ after rotation, we have $(2,1)$.

For the translation problem

When a point $(x,y)$ is translated 5 units left and 3 units down, the x - coordinate is decreased by 5 (new x = $x - 5$) and the y - coordinate is decreased by 3 (new y = $y - 3$).

Answer:

For the first question: C. (2,1)
For the second question: B. The x - coordinates decrease by 5, and the y - coordinates decrease by 3.