Question

The vertices of triangle PQR have coordinates P(2,3), Q(3,8), and R(7,3). Under which transformation of triangle PQR are distance and angle measure preserved?(1) (x,y) → (2x,3y)(2) (x,y) → (x+2,3y)(3) (x,y) → (2x, y+3)(4) (x,y) → (x+2,y+3)

Answer 1

The transformation represented in option (4) is a translation of the figure, 2 units right and 3 units up, the translation would look like this:

P(2,3) → P'(4,6)

Q(3,8) → Q'(5,11)

R(7,3) → R'(9,6)

Let's plot the to see if the length of the sides and the angles change:

As you can see, the new triangle looks exactly the same, it just moved a little upward. Then, under the transformation (4) (x,y) → (x+2,y+3) distance and angle measure are preserved​